Question

You are currently 30 years old. You intend to retire at age 60, and you want to be able to receive a 20-year, $100,000 beginning-of-the-year annuity, with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday.

A. If you expect your investments to earn 12% per year over the next 15 years and 10% per year thereafter, how much must you accumulate by the time you reach age 45?

B. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming you currently have $10,000 available to meet your goal? Assume the conditions stated in section A.

Answer 1

Answer A:

Let us first calculated fund required at age 60:

Beginning of year annuity = $100,000

Duration = 20 years

Interest rate = 10%

Required PV at age 60 = PV (rate, nper, pmt, fv, type)

= PV (10%, 20, -100000, 0,1)

= $936,492.01

Accumulated fund required at age 45 = PV = FV / (1 + Rate of interest) ^{Number of years}

= 936,492.01 / (1 + 10%) ¹⁵

= $224,188.74

Accumulated fund required at age 45 = $224,188.74

Answer B:

Current amount available = $10,000

Fund required at the age of 45 = $224,188.74

Rate of interest = 12%

Time period = 15 years

To get annual end of year deposit, we will use PMT function

=PMT (rate, nper, pv, fv, type)

= PMT (12%, 15, -10000, 224188.74,0)

= $4545.45

Annual amount must you save at the end of each of the next 15 years = $4,545.45