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.
, where r is the radius.