Question

You are 21 year-old now and planning for your retirement. You are healthy and therefore expect to live long years. Based on your forecast, you feel that a monthly income of $10,000 starting at the age of 65 (at the end of 1st month) until the 90 year-old age will be enough. Assuming annual interest rate is 8% in the distribution period and 7% in the accumulation period, how much monthly contributions will be sufficient if you start to contribute at the end of this month (month-end contributions)?

Select one:

a. $367.52

b. none of the above

c. $449.06

d. $343.84

e. $608.64

Answer 1

Step 1

In step 1 we will calculate the fund value required at the age of 65 years to get monthly income of $10000 till age of 90 years.

We can use present value of annuity to calculate the fund value.

Present value of annuity = P * {[1 - (1+r)^-n]/r}

Present value of annuity = fund value required at the age of 65 years = ?

P = annuity amount i.e.monthly income = $10000

r = rate of interest per month i.e.interest rate in the distribution period = 8%/12 = 0.0067

n = no.of months = 25 years * 12 = 300

Present value of annuity = 10000 * {[1 - (1+0.0067)^-300]/0.0067}

Present value of annuity = 10000 * {0.863763/0.0067}

Present value of annuity = 1295645.23

Fund value required at the age of 65 years = $12,95,645.23

Step 2

Treating the fund value calculated in step 1 as future value of annuity i.e.future value of monthly contribution , we can

calculate the monthly contribution amount using future value of annuity formula.

Future value of annuity = P * {[(1+r)^n -1]/r}

Future value of annuity = $12,95,645.23

P = annuity amount i.e.monthly contribution = ?

r = rate of interest per month i.e.interest rate in the accumulation period = 7%/12 = 0.005833

n = no.of months = 44 years * 12 = 528

1295645.23 = P * {[(1+0.005833)^528 -1]/0.005833}

1295645.23 = P * {20.56456/0.005833}

1295645.23 = P * 3525.354

P = 367.52

Month end contribution required = $367.52

The answer is Option a.