Final answer:
To find out how much was borrowed for the coat, we use the present value of an annuity formula, inputting the monthly payment of $72, an annual interest rate of 16% compounded monthly, for a total of 2 years. Calculating this provides the initial amount borrowed for the coat.
Step-by-step explanation:
To determine how much a person borrow to buy the coat, we can use the formula for the present value of an annuity, because the payments are made at regular intervals (monthly) and the interest is compounded monthly. The present value (PV) formula for an annuity is:
PV = PMT [ (1 - (1 + r/n)^(-nt)) / (r/n) ], where:
- PMT = monthly payment amount
- r = annual interest rate
- n = number of times the interest is compounded per year
- t = number of years
In this case, PMT = $72, r = 0.16, n = 12 (since the interest is compounded monthly), and t = 2. Plugging these values into the formula, we get:
PV = 72 [ (1 - (1 + 0.16/12)^(-12*2)) / (0.16/12) ]
Calculating this, we find the present value, which is the amount this person borrowed to buy the coat. This result will give us a sense of how much the initial coat purchase was before interest.