Question

Assume you are now 25 years old. You plan to retire when you are 65 years old. You think you will live until you are 80 years.

a.) If the rate of return during your working years (a.k.a. the "savings period") is 8% and you plan to save $2,000 per year, how much will you have saved up by retirement age?

b.) If the rate of return during your retirement is 6% on the amount of savings you have accumulated, how much will you receive as an annual income during the 15 years you are retired?

c.) Assume borrow $75,000 for college and have to pay back the loan monthly for 10 years after graduation. If the annual rate is 6%, what is the amount of your monthly loan payment?

d.) Would you rather receive: $5000 in three years, $1,000 per year for 7 years or $8000 per year for 15 years if the discount rate is 20%?

Answer 1

(a) Number of Years till retirement = n = 65 - 25 = 40 years

Investment per year = P = $2000

Rate of interest = r = 8%

FV = P[(1+r)ⁿ -1]/r = 2000(1.08⁴⁰ -1)/0.08 = $518113.04

(b) Rate of return = r = 6%

Number of Years = n = 15

Let amount received per year = X

PV is the value that we calculated above = $518113.04

=> PV = P[1- (1+r)^-n]/r

=> 518113.04 = X(1 - 1.06^-15)/0.06

=> X = $53346.35

(c) Interest Rate = 6% annual = 0.06/12 monthly = 0.005

Loan Amount = $75000

Repayment Period = n = 10*12 = 120 months

Monthly Payment = rP(1+r)^N/[(1+r)^N-1] = (0.005)*75000*1.005¹²⁰/(1.005¹²⁰ - 1) = $832.65

(d) Option 1 : 5000 in 3 years

=> NPV = 5000/1.20³ = $2893.52

Option 2 : $1,000 per year for 7 years

=> NPV = P[1- (1+r)^-n]/r = 1000(1 - 1.20^-7)/0.20 = $3604.59

Option 3 : 8000 per year for 15 years

=> NPV = P[1- (1+r)^-n]/r = 8000(1 - 1.20^-15)/0.20 = $37403.78

Hence, Option 3 is the best option