Question

Problem 1: Borrowing and Saving

In this problem, you can assume it is instant and costless to add or remove money from your

savings account and to borrow or repay credit card debt. Furthermore, assume your risk-free

savings account pays 1% interest annually, your credit card charges 12% interest annually,

and that you have no other assets or debts.

(a) Imagine you have $5,000 in your savings account and a $0 balance on your credit card.

What is the most you would pay today to receive $1,000 in 2 years?

What is the most you would pay today:

(b) Imagine you have $0 in your savings account and a $5,000 balance on your credit card.

What is the most you would pay today to receive $1,000 in 2 years?

What is the most you would pay today:

(c) If you were in the situation in described in part (b) and someone o ered you a guaranteed

$1,000 in 2 years at the cost of $700 today, would you accept? Explain how would you pay

the $700 required today, and provide a calculation showing quantitatively this is a good/bad

deal for you?

(d) Imagine you have $1,000 in your savings account and a $2,000 balance on your credit

card. How much extra money would you have in 2 years by using the $1,000 in your savings

to repay your credit card loan when compared to leaving it in your savings account for the

full two years?

Answer 1

Solution :-

1) In this case, since I have $5000 in saving account, I can pay today from my savings bank account and receive $1000 back in 2 years in my savings account.

So the interest rate to be considered is the saving interest rate which is 1%

So the maximum today actual sum is : 1000/(1+1%)² = $980.30

2) In this case since savings bank account balance is $0, I have to borrow from credit card and the relevant interest rate is 12%

So the maximum today actual sum is : 1000/(1+12%)² = $797.19

3) In this case after paying 700 today

Loss of Interest of saving account = 700*1% = 70 in year 1

770*1% = 77 in year 2

Credit card interest = 700*12%*2 = 168

Therefore the total loss in 2 years = 315 and extra amount received is 300 so it is not a good deal

4) In this case the balance in saving is 1000$ and the balance of credit card is 2000$

the extra money have in 2 years by using the $1,000 in your savings

to repay your credit card loan when compared to leaving it in your savings account for the

full two years is :-

The balance loan of credit card after 2 years = 2000*112% = 240 in year 1

and the balance loan after 2nd year = 2240*112% = 2508.8

Therefore the extra amount in saving account after 2 years for paying the credit card loan is

= 2508.8 - 1000 = 1508.8 $