Question

assignment 9 - borrowing money

1. marie is buying a new snowmobile that costs $11 500.00. she will take a loan from her bank at 4.75% for 4 years.

a) calculate maries monthly payment.
b) calculate the total amount marie will pay for the loan over the 4 years.
c) calculate maries finance charge on the loan.

1. tim wants to buy a used car that costs $3900.00. he has saved $1500.00 for a down payment on the car.

a) how much will tim have to borrow from the bank to buy the car?
b) tim can get a loan at 3.25% for 3 years from his bank. what will his monthly payment be?
c) what is the total amount tim will pay for the loan over the 3 years?
d) how much will tim pay in total for the car?

Explanation:

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Marie's Loan (1)

Step1: Define loan variables

Principal $P = 11500$, annual rate $r = 0.0475$, total months $n = 4 \times 12 = 48$, monthly rate $i = \frac{0.0475}{12}$

Step2: Calculate monthly payment

Use loan payment formula: $M = P \times \frac{i(1+i)^n}{(1+i)^n - 1}$
$M = 11500 \times \frac{\frac{0.0475}{12}(1+\frac{0.0475}{12})^{48}}{(1+\frac{0.0475}{12})^{48} - 1} \approx 263.22$

Step3: Calculate total loan payment

Total = Monthly payment × total months
$\text{Total} = 263.22 \times 48 = 12634.56$

Step4: Calculate finance charge

Finance charge = Total paid - Principal
$\text{Finance Charge} = 12634.56 - 11500 = 1134.56$

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Tim's Loan (2)

Step5: Calculate loan amount

Loan = Car cost - Down payment
$\text{Loan} = 3900 - 1500 = 2400$

Step6: Define Tim's loan variables

Principal $P = 2400$, annual rate $r = 0.0325$, total months $n = 3 \times 12 = 36$, monthly rate $i = \frac{0.0325}{12}$

Step7: Calculate Tim's monthly payment

$M = 2400 \times \frac{\frac{0.0325}{12}(1+\frac{0.0325}{12})^{36}}{(1+\frac{0.0325}{12})^{36} - 1} \approx 70.12$

Step8: Calculate Tim's total loan payment

$\text{Total Loan Payment} = 70.12 \times 36 = 2524.32$

Step9: Calculate total car cost

Total = Down payment + Total loan payment
$\text{Total Car Cost} = 1500 + 2524.32 = 4024.32$

Answer:

1. Marie's loan:

a) Monthly payment: $\$263.22$
b) Total loan payment over 4 years: $\$12634.56$
c) Finance charge: $\$1134.56$

1. Tim's loan:

a) Amount to borrow: $\$2400$
b) Monthly payment: $\$70.12$
c) Total loan payment over 3 years: $\$2524.32$
d) Total cost for the car: $\$4024.32$