Question

Question 6:
You would like to have $1,000,000 in your retirement account 35 years from now. You have saved $15,000 so far. Assume you can earn 7.0% per year. How much will you have to save each month to reach your goal?

a) $459.40

b) $651.06

c) $6,075.45

d) $8,392.47

e) $585.27

Answer 1

Present value (P. V. ) of retirement amount = Amount * (1/(1+r)^n)

Here,

r = 7% or 0.07, n = 35 years

P. V. Of retirement amount = $1000000 * (1/(1+0.07)^35)

P. V. Of retirement amount = $1000000 * 0.0937 = $93700

Now,

Net amount required today = P. V. Of retirement amount - Saving = $93700 - $15000 = $78700

Annual savings required = Net required amount / ((1 - (1/(1+r)^n))/ r)

Annual savings required = $78700 / ((1 - (1/(1+0.07)^35)) / 0.07)

Annual savings required = $78700 / 12.9477

Annual savings required = $6078.30

Monthly savings required = Annual savings / 12 months = $6078.30 / 12 = $506.53

Ans: a) $459.40

Note: Above differences in answer is due to decimals rounding off.