Question

Your parents will retire in 27 years. They currently have $390,000 saved, and they think they will need $1,950,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

  

You have $20,883.76 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $290,000. You expect to earn 13% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.

Answer 1

1]

future value = present value * (1 + r)^t

where r = annual rate of interest

t = number of years

$1,950,000 =  $390,000 * (1 + r)²⁷

r = ($1,950,000 / $390,000)^1/27 - 1

r = 6.14%

2]

Number of years to reach goal is calculated using NPER function in Excel :

rate = 13%

pmt = -5000 (Annual deposit. This is entered with a negative sign because it is a cash outflow)

pv = -20883.76 (Amount in account today. This is entered with a negative sign because it is like a cash outflow today)

fv = 290000 (Required ending value of account)

NPER is calculated to be 14

It will take 14 years to reach goal