Question

You want to make a one-time deposit into a bank account today and have $2,000 in the account in five years.

Which interest rate requires you to deposit the least amount of money into the account today?

Show your work.

a.) 1%

b.) 8%

c.) 5%

d.) 4%

Answer 1

B) 8%

Explanation: The higher the interest rate , lower will be the present value of the amount along with the money to be deposited today.

Rate = 1%

Pv= Future value / (1+r)^n

= 2,000 / (1.01)^5

= 2,000 / 1.051

= $1,902.93

Rate = 8%

Pv= Future value / (1+r)^n

= 2,000 / (1.08)^5

= 2,000 / 1.4693

= $1,361.66

Rate = 5%

Pv= Future value / (1+r)^n

= 2,000 / (1.05)^5

= 2,000 / 1.2763

= $1,567.03

Rate = 4%

Pv= Future value / (1+r)^n

= 2,000 / (1.04)^5

= 2,000 / 1.2167

= $1,643.78

As we can see from the above calculation, the least amount of present value of amount $2,000 is at 8% interest rate. So, we should deposit at 8% to get 2,000 at the end of year 5 .