Question

Keiko is looking at the following investment choices and wants to know what annual rate of return each choice produces. a.  Invest ​$450.00 and receive ​$666.54 in 9 years. b.  Invest ​$2 comma 600.00 and receive ​$11,433.61 in 14 years. c.  Invest ​$32,894.72 and receive ​$100,000.00 in 20 years. d.  Invest ​$32,401.38 and receive ​$1,500,000.00 in 45 years.

Answer 1

Choice 1:

Amount invested = $450.00
Amount received = $666.54
Period = 9 years

Amount invested * (1 + Interest rate)^Period = Amount received
$450.00 * (1 + Interest rate)^9 = $666.54
(1 + Interest rate)^9 = 1.48120
1 + Interest rate = 1.0446
Interest rate = 0.0446 or 4.46%

Choice 2:

Amount invested = $2,600.00
Amount received = $11,433.61
Period = 14 years

Amount invested * (1 + Interest rate)^Period = Amount received
$2,600.00 * (1 + Interest rate)^14 = $11,433.61
(1 + Interest rate)^14 = 4.39754
1 + Interest rate = 1.1116
Interest rate = 0.1116 or 11.16%

Choice 3:

Amount invested = $32,894.72
Amount received = $100,000.00
Period = 20 years

Amount invested * (1 + Interest rate)^Period = Amount received
$32,894.72 * (1 + Interest rate)^20 = $100,000
(1 + Interest rate)^20 = 3.04000
1 + Interest rate = 1.0572
Interest rate = 0.0572 or 5.72%

Choice 4:

Amount invested = $32,401.38
Amount received = $1,500,000.00
Period = 45 years

Amount invested * (1 + Interest rate)^Period = Amount received
$32,401.38 * (1 + Interest rate)^45 = $1,500,000.00
(1 + Interest rate)^45 = 46.29432
1 + Interest rate = 1.0890
Interest rate = 0.0890 or 8.90%