Question

f 7. will has a goal of $5,000,000. To achieve this goal, he invests S 1,000 each month. If Will can earn .75% per month, the time it will take him to reach his goal is closest to... (5) a) 30.2 years b) 32.1 years c) 35.7 years d) 40.7 years e) 42.4 years Plese dlo no Use exce thanks 43.8 years g) 45.5 years h) 51.9 years i) greater than 100 years

Answer 1

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.