Attempts 0 8 Implied interest rate and period Consider the c

Attempts: 0 8. Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or Keep the Highest: 0/1 Aa Aa duration. Ryan needed money for some unexpected expenses, so he borrowed $3,111.72 from a friend and agreed to repay the loan in five equal installments of $800 at the end of each year. The agreement is offering an implied interest rate of Ryan\'s friend, Adam, has hired a financial planner for advice on retirement. Considering Adam\'s current expenses and expected future lifestyle changes, the financial planner has stated that once Adam crosses a threshold of $15,636,432 in savings, he will have enough money for retirement. Adam has nothing saved for his retirement yet, so he plans to start depositing $85,000 in a retirement fund at a fixed rate of 9.00% at the end of each year. It will take years for Adam to reach his retirement goal. Flash Player WI 30,0,0,134 6 2013 Conigoge Leeming et as noted All rights rod 34.1 # 2004-2016 Apt; All rights reserved Grade It Now Save & Continue

Solution

Answer a.

Amount borrowed = $3,111.72
Annual Payment = $800
Period = 5 years

Let annual interest rate be i%

$3,111.72 = $800 * PVIFA(i%, 5)

Using financial calculator:
N = 5
PV = -3111.72
PMT = 800
FV = 0

I = 9%

So, implied interest rate is 9.00%

Answer b.

Desired sum = $15,636,432
Annual saving = $85,000
Annual interest rate = 9.00%

Let n be the number of years required to reach the desired goal.

$15,636,432 = $85,000 * FVIFA(9.00%, n)

Using financial calculator:
I = 9.0%
PV = 0
PMT = -85000
FV = 15636432

N = 33.25

So, it will take 33.25 years for Adam to reach his retirement goal.