QUESTÃO CERTA: Pelo método de amortização constante, os juros pagos mensalmente se reduzem bem como o valor das prestações.
QUESTÃO ERRADA: No sistema de amortização constante (SAC), o valor das parcelas pagas pelo empréstimo é constante ao longo de todo o tempo de contrato do empréstimo.
Gabarito ERRADO
SAC = amortização constante
Sistema Price = parcela constante
QUESTÃO CERTA: Paulo decidiu comprar a prazo um veículo zero quilômetro que custa R$ 41 mil. A respeito das opções de empréstimos sugeridas a Paulo, julgue o item subsecutivo. Caso Paulo financie o valor total do veículo pelo sistema de amortização constante, em 5 prestações mensais e consecutivas, vencendo a primeira prestação um mês após a data do financiamento e a juros de 3% ao mês, então o valor da segunda prestação desse financiamento será superior a R$ 9.150.
Amortização = R$ 41.000/5
Amortização = R$ 8.200,00
Juros = R$ 41.000 x 0,03
Juros = R$ 1.230,00
1 parcela = Amortização + juros
1 parcela = R$ 9.430,00
2 parcela = amortização + juros do saldo devedor após o pagamento da 1 amortização
Juros = ( R$ 41.000,00 – R$ 8.200,00 ) x 0,03
Juros = R$ 32.800,00 x 0,03
Juros = R$ 984,00
2 parcela = amortização + juros
2 parcela = R$ 8.200,00 + R$ 984,00
2 parcela = R$ 9.184,00
R$ 9.184,00 > R$ 9.150,00
QUESTÃO ERRADA: Para pagar uma obra em 20 prestações iguais, mensais e consecutivas de R$ 30.000,00, um condomínio fixou a taxa extra de R$ 50,00 mensais para cada uma de suas 800 unidades. Com base nessas informações, julgue o item a seguir. Se a obra ficar em R$ 500.000,00, para pagamento em 20 prestações mensais pelo sistema de amortização constante, sem prazo de carência e com taxa de juros compostos de 2% ao mês, a nona prestação será inferior a R$ 30.000,00.
SD 500.000
Amortização = 500.000/20= 25.000
Amortização =25.000
Juros= 500.00*2/100= 10.0000
P1= Amort+Juros
P1= 25.000+10.000=35.000
r= 25.000*2/100=500
P9=P1-n*r
P9= 35.000-8*500
P9= 35.000-4000. P9= 31.000
QUESTÃO CERTA: Situação hipotética: Um banco emprestou R$ 12.000 para Maria, que deve fazer a amortização em doze parcelas mensais consecutivas pelo sistema de amortização constante sem carência. A taxa de juros contratada para o empréstimo foi de 1% ao mês, e a primeira parcela deverá ser paga um mês após a tomada do empréstimo. Assertiva: O valor da quarta parcela a ser paga por Maria é de R$ 1.090.
No sistema SAC, em cada parcela a amortização é de A = VP/n = 12.000 / 12 = 1.000 reais.
Após pagar 3 parcelas, já foram amortizados 3×1.000 = 3.000 reais, havendo um saldo devedor de 12.000 – 3.000 = 9.000 reais.
Durante o 4º período este saldo rende juros de 1%, ou seja:
Juros = 1% x 9.000 = 90 reais
Assim, a quarta prestação é:
P = A + J
P = 1.000 + 90 = 1.090 reais
Resposta: C
QUESTÃO ERRADA Com relação a sistemas de amortização de empréstimos e financiamentos, julgue o item a seguir. Situação hipotética: Uma instituição bancária concedeu empréstimo de R$ 30.000, entregues no ato, sem prazo de carência, para ser quitado pelo sistema de amortização constante em 24 prestações mensais. A primeira prestação vencerá um mês após a tomada do empréstimo, sendo de 2% a taxa de juros mensais adotada pela instituição bancária. Assertiva: Nessa situação, as prestações são decrescentes e a diferença entre duas prestações consecutivas é igual a R$ 50.
SAC
Valor da amortização => (Principal/Número de Prestações) => 30.000/24 = 1.250
Valora da parcela => (juros x saldo devedor + amortização)
Parcela 1 => 0,02×30.000 + 1.250 = 600 + 1250 = 1850
Parcela 2 => 0,02×28.750 + 1.250 = 575 + 1250 = 1825
Parcela 3 => 0,02×27.500 + 1.250 = 550 + 1250 = 1800
.
.
.
Última Parcela => 0,02×1.250 + 25 = 25 + 1250 = 1275
Ou seja, as parcelas são decrescentes e a diferença entre elas é de R$ 25. Pode ser calculado simplesmente calculando o montante de juros sobre a última prestação ou fazendo a diferença entre duas prestações quaisquer.
QUESTÃO ERRADA: Um financiamento de R$ 10.000 foi feito pelo sistema de amortização constante (SAC) em 5 meses consecutivos e com 2 meses de carência. A operação foi contratada à taxa de juros de 8% ao mês. Nessa situação, o valor da segunda prestação após o início da amortização era inferior a R$ 2.500.
Se temos 2 meses de carência, durante os primeiros dois meses não é pago nenhum valor, e o saldo deve ser acrescido dos juros, chegando a M = 10.000 x (1,08)^2 = 10.000 x 1,1664 = 11.664 reais.
A partir daí começamos o financiamento propriamente dito, cujo pagamento se dá em 5 prestações. A amortização em cada prestação é de 11.664 / 5 = 2.332,80 reais.
Após o pagamento da primeira prestação, o saldo devedor cai para 11.664 – 2.332,80 = 9331,20 reais. Assim, os juros incidentes ao longo do mês da segunda prestação são de 8% x 9331,20 = 746,49 reais. E assim, a segunda prestação totaliza 746,49 + 2332,80 = 3079,29 reais, que é SUPERIOR a 2.500 reais.
QUESTÃO CERTA: Ao se efetuar o pagamento de um empréstimo de R$ 100.000,00 pelo sistema SAC, em 10 prestações — mensais, consecutivas e com a 1.ª prestação vencendo um mês após a tomada do empréstimo — e com juros de 10% ao mês, o valor da 5.ª prestação será R$ 16.000,00.
No SAC, para encontrar o valor amortizável usaremos a fórmula: A = E/n, em que A é o valor amortizável (sempre fixo, pois a amortização é constante), E é o valor que será amortizado e “n” será o número de parcelas.
A = 100.000/10
A = 10.000
Como amortizaremos 10.000 por mês, o valor da 5ª parcela será o valor remanescente após o pagamento da 4ª parcela (R$ 60.000).
Multiplicamos 60.000 x 0,1 (valor da tx mensal) = 6.000 (de juros)
Valor da parcela =
A + J
10.000 + 6.000
= 16.000
QUESTÃO CERTA: Um banco emprestou R$ 200.000, entregues no ato, sem prazo de carência. O empréstimo foi quitado pelo sistema de amortização constante (SAC) em 20 prestações semestrais consecutivas. Nessa situação, se a taxa de juros do empréstimo foi de 1,5% ao semestre, então o valor da quinta prestação, em reais, foi de: 12.400.
A = 200.000/20
A = 10.000
J = 200.000 * 1,5%
J = 3.000
P1 = A+J
P1 = 10.000 + 3.000
P1 = 13.000
Como no SAC a Amortização é constante, sabemos que ao final da 4ª parcela teremos amortizado o valor de 40.000,00 daqui já podemos ir direto para o cálculo da 5ª parcela:
SD = 200.000 – 40.000
SD = 160.000
J = 160.000 * 1,5%
J = 2.400
P5 = 10.000 + 2.400
P5 = 12.400
QUESTÃO CERTA: Recentemente, a empresa Fast Brick Robotics mostrou ao mundo um robô, conhecido como Hadrian 105, capaz de construir casas em tempo recorde. Ele consegue trabalhar algo em torno de 20 vezes mais rápido que um ser humano, sendo capaz de construir até 150 casas por ano, segundo informações da empresa que o fabrica.
Internet:<www.fastbrickrobotics.net> (com adaptações).
Tendo como referência as informações acima, julgue o item a seguir.
Situação hipotética: Para comprar uma casa construída pelo robô, uma pessoa contraiu um empréstimo de R$ 120.000,00, a ser pago pelo sistema de amortização constante (SAC) em 6 anos, em 12 prestações semestrais, com taxa de juros semestral de 8%.
Assertiva: Nesse caso, desconsiderando-se a existência de eventual prazo de carência, o valor da prestação a ser paga ao final do quarto semestre será superior a R$ 16.000,00.
Sobre SAC, cujas amortização serão sempre iguais, e sabendo que os juros ou as parcelas formam uma PA, logo:
SD = 120.000
n = 6 anos = 12 semestres
i = 8% a.s.
Amortização = SD/n = 120.000/12 = 10.000
Saldo devedor após o pagamento da 3ª parcela:
SD = 120.000
– 3 x 10.000
SD = 120.000
– 30.000 = 90.000
Juros da 4ª parcela:
Juros = 90.000 x 0,08 = 7.200
Portanto, o valor da 4ª parcela será:
4ª parcela = 10.000 + 7.200 = 17.200, ou seja, será MAIOR que 16.000.
QUESTÃO CERTA: A respeito de sistemas de amortização e de taxas de juros de empréstimos bancários, julgue o item a seguir. Uma das características do sistema de amortização constante (SAC) é que as prestações a serem pagas pelo tomador do empréstimo são todas iguais.
O SAC as prestações vão diminuindo com o tempo. O valor da parcela é a seguinte: Amortização + Juros.
O sistema em que as parcelas são constantes é o Price (francês).
QUESTÃO ERRADA: Um indivíduo contratou um financiamento imobiliário no valor de R$ 120 mil com juros nominais de 12% a.a., capitalizados mensalmente e com prazo de 40 meses para amortização. Nesse contrato de financiamento, não há atualização monetária prevista. Com base nessa situação, julgue os seguintes itens, considerando 32,8347 como valor aproximado de [1,0140 – 1]/[0,01 × 1,0140 ]. A partir do 19.o mês de financiamento, o valor da prestação mensal do financiamento imobiliário pelo sistema de amortização constante (SAC) será inferior ao valor da prestação calculado pelo sistema francês, tomando-se, para ambos os sistemas, uma taxa de juros efetiva de 1% a.m.
PRICE
VP= P * [(1 + i)^t – 1 / (1 + i)^t * i]
120000= P * [(1,01)^40 – 1 / (1,01)^40 * 0,01]
120000= P * 32,8347
P= 3654,67
SAC
A= VP/ t
A= 120000/ 40
A= 3000
P (prestação= juros + amortização) = [ 1+ (t- t 19 +1) * i ] * A
P= [ 1+ (40- 19 +1) * 0,01 ] * 3000
P= [ 1+ (22) * 0,01 ] * 3000
P= [ 1+ 0,22 ] * 3000
P= [ 3000+ 660 ] = 3660
ERRADO
QUESTÃO CERTA: No que se refere ao sistema de amortização constante (SAC) e ao sistema de amortização francês — tabela Price —, julgue o item que segue. Se um empréstimo de R$ 1.200 for contratado para ser pago em 12 parcelas mensais e consecutivas pelo SAC à taxa de juros de 2% ao mês, e se a primeira prestação for paga 1 mês após a contratação, o valor da terceira prestação será de R$ 122.
Saldo Inicial Juros Amortização Parcela
1.200 24 100 124
1.100 22 100 122
1.000 20 100 120
Lembrar 1.200 / n = Amortização, logo 100. Juros = Saldo Inicial x i
A= C/n
A= 1.200/12
A= 100
P3= A+( SD2 X i) SD2= Saldo devedor anterior
P3= 100+ (1000.0,02)
P3= 100+ 20
P3= 120
QUESTÃO ERRADA: Um banco emprestou R$ 10.000,00 à taxa de juros mensais de 1%, devendo ser pago pelo sistema de amortização constante (SAC), em 10 parcelas mensais e consecutivas, com a primeira prestação vencendo um mês após a tomada do empréstimo (sem carência). Nessa situação, o valor da primeira prestação será superior a R$ 1.150,00.
A= 10.000/10 (n º parcela) = 1.000
P1= 1000+10.000(0,01) 1.100 (E)
QUESTÃO CERTA: Um banco emprestou a uma empresa R$ 100.000, entregues no ato, sem prazo de carência, para serem pagos em quatro prestações anuais consecutivas pelo sistema de amortização constante (SAC). A taxa de juros compostos contratada para o empréstimo foi de 10% ao ano, e a primeira prestação será paga um ano após a tomada do empréstimo. Nessa situação, o valor da segunda prestação a ser paga pela empresa será: superior a R$ 32.000 e inferior a R$ 33.000.
SD = 100.000
A = 100.000/4 = 25.000
i = 10% a.a
P2 = ??
P2 = A + J2
P2 = 25.000 + (100.000-25.000) x 0,1
P2 = 25.000 + 75.000×0,1
P2 = 25.000 + 7500
P2 = 32.500
QUESTÃO CERTA: Uma dívida de R$ 5.000,00 foi paga, em 5 prestações mensais e consecutivas pelo Sistema de Amortização Constante (SAC), sem prazo de carência. Sabendo que a 2.a prestação paga foi de R$ 1.240,00, julgue os itens que se seguem a respeito do plano de amortização dessa dívida. A 5.a prestação paga foi superior a R$ 1.100,00.A soma dos juros pagos nas 5 prestações foi de R$ 900,00.
QUESTÃO ERRADA: Uma dívida de R$ 2.000,00 foi paga, com juros de 5% ao mês, em 4 meses, pelo sistema de amortização constante (SAC); a primeira prestação venceu em um mês após a tomada do empréstimo. Considerando essas informações, julgue o item que se segue. O valor pago pela primeira prestação foi de R$ 550,00.
QUESTÃO CERTA: Situação hipotética: Um cliente tomou R$ 60.000 de empréstimo em um banco. A quantia foi entregue no ato, sem prazo de carência, e deverá ser quitada pelo sistema de amortização constante (SAC) em 12 prestações mensais consecutivas e com a primeira prestação vencendo um mês após a tomada do empréstimo. A taxa de juros contratada foi de 2% ao mês. Assertiva: Nesse caso, o valor da sexta prestação será de R$ 5.700.
Construindo uma tabela de SAC:
Dívida: 60.000 – prazo: 12 meses = 5.000 / mês
Passos para a construção da tabela:
1 – Meses
2 – Amortização: 5.000 / mês
3 – Saldo
4 – Juros sobre o saldo (2%)
5 – Parcela
Meses Saldo Juros Amortização Parcela
1 60.000 1.200 5.000 6.200
2 55.000 1.100 5.000 6.100
3 50.000 1.000 5.000 6.000
4 45.000 900 5.000 5.900
5 40.000 800 5.000 5.800
6 35.000 700 5.000 5.700
QUESTÃO CERTA: Uma dívida de R$ 5.000,00 foi paga, em 5 prestações mensais e consecutivas pelo Sistema de Amortização Constante (SAC), sem prazo de carência. Sabendo que a 2.a prestação paga foi de R$ 1.240,00, julgue os itens que se seguem a respeito do plano de amortização dessa dívida. A soma dos juros pagos nas 5 prestações foi de R$ 900,00.
QUSTÃO CERTA: Um banco emprestou R$ 10.000,00 à taxa de juros mensais de 1%, devendo ser pago pelo sistema de amortização constante (SAC), em 10 parcelas mensais e consecutivas, com a primeira prestação vencendo um mês após a tomada do empréstimo (sem carência). Nessa situação, o total dos juros pagos até a quinta prestação inclusive será igual a R$ 400,00.
PV = R$ 10.000,00 i= 1%> 0.01 Parcelas > 10x (10.000/10= 1.000 amortização)
n Parcelas (Juros + Atual) Juros Amortização Saldo Devedor
0 ——— — —— 10.000
1 1.100 100 1.000 9.000
2 1.090 90 1.000 8.000
3 1.080 80 1.000 7.000
4 1.070 70 1.000 6.000
5 1.060 60 1.000 5.000
T 5.400 400 5.000 —–
QUESTÃO CERTA: Suponha que um casal pretenda adquirir imóvel no valor de R$ 500 mil, sem entrada e sem diferimento da primeira parcela, adotando o sistema de amortização constante como metodologia de apuração das prestações e consiga no banco prazo de vinte anos e dez meses à taxa nominal de 12% ao ano. Nessa situação, o valor da décima segunda parcela será inferior a R$ 7 mil.
20 anos e 10 meses correspondem a 250 meses. Assim, a amortização
Mensal é:
A = VP / n = 500000 / 250 = 2000 reais
Após pagar 11 prestações, o saldo devedor é:
SD = 500000 – 11 x 2000
SD = 478000 reais
A taxa de juros nominal de 12% ao ano corresponde à taxa efetiva de
12% /12 = 1% ao mês. Assim, os juros do 12º mês são:
J = 1% x 478000
J = 4780 reais
A 12ª prestação é:
P = A + J
P = 2000 + 4780
P = 6780 reais
Item CORRETO.
QUESTÃO ERRADA: Eduardo abriu, em 5/4/2010, uma conta remunerada que paga juros compostos de 10% ao ano. Nos dias 5/4/2010, 5/4/2011 e 5/4/2012, ele depositou, nessa conta, uma mesma quantia, de modo que esses três depósitos foram os únicos feitos na conta. No dia 5/3/2013, Eduardo fez um empréstimo de R$ 60.000,00, o qual deve ser quitado pelo sistema de amortização francês (SAF) em 20 prestações mensais, iguais e consecutivas de R$ 3.641,00, com a primeira prestação vencendo um mês após a tomada do empréstimo. Com base nessas informações, julgue os itens subsecutivos, considerando 18 como valor aproximado para 1/1,01 + 1/1,012 + … + 1/1,0120. Se, ao invés do SAF, o financiamento for pago pelo sistema de amortização constante, em 20 prestações, mensais e consecutivas, à taxa de juros compostos de 5% ao mês, então o valor da décima prestação será inferior a R$ 4.500,00.
C= 60.000
t= 20 meses
A=60.000/20=3.000
i=0,05
Na décima prestação ele terá pago somente 9 prestações, faltando portanto, 11 cotas de amortização, logo saldo devedor após o pagamento da 9ª prestação é 11*3.000=33.000
P=J+A
P=(0,05*33.000)+3.000=
P= 1.650+3.000= 4.650,00
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