## Answers

We have the following information

Future Amount (F) = $5,000,000

Annual Investment = $1,000 × 12 = $12,000

Interest rate = 0.75% per month

First, we will convert the monthly interest rate into annual rate

Effective annual interest rate (i) = ((1 + 0.0075)^{12} – 1) × 100

Effective annual interest rate (i) = 9.4% or 0.094

F = A[((1 + i)^{n} – 1)/i]

F = A(F/A, i, n)

(F/A, i, n) = Equal payment series compound amount factor

A = Equal amount deposited at the end of each interest period

n = Number of interest periods

i = Interest rate

F = Single future amount

F = 5,000,000

A = 12,000

n = ?

i = 9.4% or 0.094

5,000,000 = 12,000(F/A, 9.4%, n)

5,000,000 = 12,000[((1 + 0.094)^{n} – 1)/0.094]

469,999 = 12,000(1.094)^{n}

Log (469,999) = Log (12,000) + nLog (1.094)

5.67 = 4.08 + (0.039)n

**n = 40.7 years**

**So, it will take 40.7 years for Will to reach his goal.**