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:

Answer 1

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