Question

6. Suppose you borrow $50,000 at a rate of 5% compounded annually and must repay it in 5 equal installments at the end of each of the next 5 years. a. How much will your first installment be? b. How much will you still owe after you pay your first installment?

Answer 1

a) Amount borrowed = 50000, Rate of interest = 5%, period of loan = 5 years

To find the equal yearly installment to be paid at the end of next 5 years, we will pmt function in excel

Formula to be used in excel: =pmt(rate,nper,-pv)

                                          =pmt5%,5,-50000)

Calculating Yearly installment
Loan (pv)	50000
Annual rate (rate)	5.00%
No of years (nper)	5
Yearly installment (pmt)	11548.74

Using pmt function in excel, we get yearly installment = 11548.74

Hence first installment = 11548.74

b) Loan at beginning of year 1 = Loan borrowed = 50000

Interest paid in 1st installment = Amount of loan at beginning of year 1 x Interest rate = 50000 x 5% = 2500

Principal paid in 1st installment = Yearly installment - Interest paid in 1st installment = 11548.74 - 2500 = 9048.74

Principal owed after payment of 1st installment = Loan at the beginning of year 1 - Principal paid in 1st installment = 50000 - 9048.74 = 40951.76

Amount still owed after payment of 1st installment = 40951.76