Question

Solve each of the following three problems, all of which involve borrowing money from a bank with an APR of 6.5% compounded annually. Look carefully at how the problems differ from one another, in spite of appearing similar. In your solutions, say a few words explaining how you can tell which is the appropriate formula to apply in each case.

a. Suppose that you borrow $1000 once per year, beginning today, and ending 10 years from now (so you borrow your last $1000 on the ten year anniversary of today’s date). How much will your total debt be at the end of the 10th year?

b. Suppose that you borrow $10,000 today. You repay the loan over the course of ten years, making a payment every year on the anniversary of today’s date. The first payment will be one year from today, and the last payment will be ten years from today. How much should each payment be?

c. Suppose that you borrow $10,000 today, and repay the loan all at once, on the ten year anniversary of today’s date. How much will you have to repay on that date?

Answer 1

a. Amount borrowed per year beginning from now =$1000, APR=6.5% compounded annually

Cash flow are given by

Year or t=	0	1	2	3	4	5	6	7	8	9	10
Cash Out Flow	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000

We have to find the value of total debt at the end of 10th year i.e. at t=10

For this we will use fv function in excel

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

                                           =fv(6.5%,10,-1000,-1000)

Calculation of total debt at t=10
Initial cash outflow at t=0 (pv)	-1000
Cash outflow from t=1 to t=10 (pmt)	-1000
No of cash outflow from t=1 to t=10 (nper)	10
APR (rate)	6.50%
Total debt at end of 10 years or at t=10	15371.56

Using fv formula in excel, we get total debt at the end of 10 years = $15371.56

b.Amount borrowed = $10000, APR = 6,5%. Period of Loan or No of years = 10 years

We will use pmt function in excel to calculate the annual payment to repay loan

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

                                          =pmt(6.5%,10,-10000)

Calculating Annual Payment to repay loan
Loan Borrowed (pv)	10000
APR(rate)	6.50%
No of Years or Period of Loan (nper)	10
Annual Payment to repay loan (pmt)	1391.05

Using pmt function in excel, we get annual payment to repay loan = $1391.05

c. Amount borrowed = $10000, APR = 6,5%. Period of Loan or No of years = 10 years

We will use fv function in excel to calculate the amount to repaid after 10 years

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

                                          =fv(6.5%,10,0,-10000)

Here in the Formula pmt =0 as there are no yearly annual payments to repay the loan

Calculating Amount to repaid after 10 years
Loan Borrowed (pv)	10000
APR(rate)	6.50%
No of Years or Period of Loan (nper)	10
Amount to repaid after 10 years (fv)	18771.37

Using fv function in excel, we get amount to be repay loan at once after 10 years = $18771.37