Question

A friend asks to borrow $55 from you and in return will pay you $58 in one year. If your bank is offering a 6.0% interest rate on deposits and​ loans: a. How much would you have in one year if you deposited the $55 ​instead? b. How much money could you borrow today if you pay the bank $58 in one​ year? c. Should you loan the money to your friend or deposit it in the​ bank?

Answer 1

Answer:

a.

Value of deposit = $58.3

b.

We can borrow approx $54.72 today if we are to pay bank $58 in one year from now.

c.

The return provided by bank for a deposit of $55 is an interest of $3.3 (58.3 - 55) while the return provided by lending to a friend is $3 (58 - 55). So, the money should be deposited in the bank.

Explanation:

a.

The interest offered by the bank is at 6% which we assume is the simple interest rate. To calculate the value one year from now of $55 deposited in the bank at 6%, we can use the following formula,

Value of deposit = Principal + Interest

Where,

Interest can be calculated as = Principal * interest rate

So,

Value of deposit = 55 + 55 * 0.06

Value of deposit = $58.3

We would have $58.3 one year from now if deposited in the bank.

b.

To calculate the money that can be borrowed today for a one year later payment of $58 can be calculated using the present value formula,

Present Value = Future Value / (1+i)^t

Present value = 58 / (1+0.06)^1

Present value = 54.71698113 rounded off to $54.72

So, we can borrow approx $54.72 today if we are to pay bank $58 in one year from now.

c.

The return provided by bank for a deposit of $55 is an interest of $3.3 (58.3 - 55) while the return provided by lending to a friend is $3 (58 - 55). So, the money should be deposited in the bank.