Question

10. Implied interest rate and period Aa Aa Consider the case of the following annuities and the need to compute either their expected rate of return or duration. David needed money for some unexpected expenses, so he borrowed $5,464.40 from a friend and agreed to repay the loan in eight equal installments of $1,100 at the end of each year. The agreement is offering an implied interest rate of David's friend, Keanu, has hired a financial planner for advice on retirement. Considering Keanu's current expenses and expected future lifestyle changes, the financial planner has stated that once Keanu crosses a threshold of $4,991,331 in savings, he will have enough money for retirement. Keanu has nothing saved for his retirement yet, so he plans to start depositing $85,000 in a retirement fund at a fixed rate of 12.00% at the end of each year. It will take years for Keanu to reach his retirement goal.

Answer 1

Answer a.

Amount borrowed = $5,464.40
Annual payment = $1,100
Number of payments = 8

Using financial calculator:
N = 8
PV = 5464.40
PMT = -1100
FV = 0

I = 12%

So, the agreement is offering an implied interest rate of 12.00%

Answer b.

Desired sum = $4,991,331
Annual deposit = $85,000
Interest rate = 12.00%

Using financial calculator:
I = 12%
PV = 0
PMT = -85000
FV = 4991331

N = 18.4 or 18

It will take 18 years for Keanu to reach his retirement goal.