Answer:
- $274.22 per month
- $2071.92 in total interest
- $433.48 more per month
- $1379.52 less in interest
Step-by-step explanation:
a) The amortization formula is used to find the monthly payment (A):
A = P(r/n)/(1 -(1 +r/n)^(-nt))
for a loan of a principal amount P at annual rate r compounded n times per year for t years.
For a borrowed amount of $7800 at 16% compounded monthly for 3 years, the payment will be ...
A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·3)) ≈ $274.22
You must pay $274.22 each month to pay off the credit card in 3 years.
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b) The total amount repaid is 36 times this monthly payment, so is ...
$274.22 × 36 = $9871.92
The amount by which this exceeds the principal borrowed is ...
$9871.92 -7800 = $2071.92
You will pay $2071.92 in interest.
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c) Changing the time period to 1 year gives the payment value ...
A = $7800(.16/12)/(1 -(1 +.16/12)^(-12·1)) ≈ $707.70
The additional amount you must pay is ...
$707.70 -274.22 = $433.48
You must pay $433.48 more each month.
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d) Your total interest with the higher payments will be ...
$707.70×12 -7800 = $692.40
The difference in interest amounts is ...
$2071.92 -692.40 = $1379.52
You will pay $1379.52 less in total interest.
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<em>Caveat</em>
Here, the monthly amounts are rounded and the total repayment amount is based on that rounded value. In an actual payment situation, the final payment will be adjusted by a small amount to account for the fact that the monthly payment shown is not exact. That will affect the total interest and the difference in interest.
is twice the product of 3 and x, and if it exceeds 
by 10, then we add 10 to 
.