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. The formula is annuity immediate. This requires annual addition at the end of each period. The total debt at the end of the 10th year is $16,248.70.

b. Amortized loan repayment is applicable here since the loan and interest are repaid every year. Therefore, the payment every year is: $1,391.05.

c. The compound interest formula is used here since the interest accumulates annually but repayment of loan is due at the end of 10 years. The total debt due for repayment at the end of the 10th year is $18,771.37.

Step-by-step explanation:

1. Data and Calculations:

Starting Principal = $1000

Annual Addition = $1000

Annual interest rate = 6.5%

Period of loan = 10 years

The formula is annuity immediate. This requires annual addition at the end of each period.

Using the annuity calculator for annual addition at the end of each period, the loan's:

End Balance $16,248.70

Total Principal $11,000.00

Total Interest $5,248.70

2. Starting Principal = $10,000

Annual interest rate = 6.5%

Period of loan = 10 years

Amortized loan repayment is applicable here since the loan and interest are repaid every year. Therefore, the payment every year is: $1,391.05

Total of 10 Payments $13,910.47

Total Interest $3,910.47

3. Starting Principal = $10,000

Annual interest rate = 6.5%

Period of loan = 10 years

Compound interest formula is used here since the interest accumulates annually but repayment of loan is due at the end of 10 years.

Using an online financial calculator, the future debt will total $18,771.37 with a total compounded interest of $8,771.37 ($18,771.37 - $10,000).

FV = $18,771.37

Total Interest $8,771.37