Question

Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be repaid in four equal annual installments. The interest paid in the first year is ________. $1,152 $ 277 $ 152 $ 420

Answer 1

Answer:

Interest paid in the first year   = $420

Explanation:

This the an example of a loan amortization. A loan amortization is a method of loan repayment where a series of equal amount (instalment) is paid by the borrower to offset both the loan principal amount and the accrued interest over the loan period.

The interest paid in a year :

This is calculated as interest rate × loan balance at the  beginning of the year

For Aunty Tilly, Interest paid in the first year will be:

         = 12% × 3500

          = $420

Equal Installment

The equal installment is calculaed as follows:

Equal amount = Loan Amount/ annuity factor

Annuity factor = (1 - (1 +r)^(-n))/ r

r- number of period, r- interest rate

Annuity factor  = 1 - (1+0.12)^(-4)/0.12)

                         = 3.0373

in this question, the equal installment:

                            = 3500/3.0373

                           =$ 1152.32 (the question did not ask for this anyway)