Question

Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal? Note: Ignore Leap Years.

Multiple Choice

• 7.67 percent

• 6.27 percent

• 9.20 percent

• 7.06 percent

• 8.54 percent

Answer 1

Number of years = 20

Value required after 20years = $1,000,000 (1 million)

Per day savings = $75

So per month Savings = $75 * 30 = $2,250

Annually savings = $2,250 * 12 = $27,000

Formula used to find future value with annual payments, P and yearly compounding for n period is as below:

FV = P * [ {(1+r)^n - 1 } / r ]

Here P = annual savings = $27,000

r = annual rate in %

n = number of years = 20

FV = $27,000 * [ {1+r)^20 - 1 } / r ]

Solving r using trial and error method, for r = 6.27%, FV = $1,022,525.94 which is close tp the required $1,000,000. All other interest rates values are as below:

interest rate	Future Value
7.67%	$1,191,322.87
6.27%	$1,022,525.94
9.20%	$1,412,716.89
7.06%	$1,114,157.20
8.54%	$1,312,020.08

Answer: r = 6.27%