Question

Time Value of Money Concept

The following situations involve the application of the time value of money concept. Use the full factor when calculating your results.

Use the appropriate present or future value table:

FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1

1. Janelle Carter deposited $9,610 in the bank on January 1, 2000, at an interest rate of 15% compounded annually. How much has accumulated in the account by January 1, 2017? Round to the nearest whole dollar.
$__________

2. Mike Smith deposited $23,480 in the bank on January 1, 2007. On January 2, 2017, this deposit has accumulated to $42,049. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit? Round to the nearest whole percent.
__________ %

3. Lee Spony made a deposit in the bank on January 1, 2010. The bank pays interest at the rate of 10% compounded annually. On January 1, 2017, the deposit has accumulated to $17,750. How much money did Lee originally deposit on January1, 2010? Round to the nearest whole dollar.
$_________

4. Nancy Holmes deposited $4,740 in the bank on January 1 a few years ago. The bank pays an interest rate of 8% compounded annually, and the deposit is now worth $9,475. How many years has the deposit been invested? Round to the nearest whole year.
_________years

Answer 1

1. Answer : $ 103,416

The amount that has accumulated by January 1, 2017 = Principal x ( 1 + r ) ¹⁷ = $ 9,610 x ( 1.15) ¹⁷ = $ 103,415.75

2. Answer: 6 %

FVIF = $ 42,049 / $ 23,480 = 1.7908

( 1 + r ) ¹⁰ = 1.7908

r = 6 %

3. Answer: $ 9,109

FV of $ 1 at 10 % for 7 years = 1.9487

Amount of deposit in 2010 = $ 17,750 / 1.9487 = $ 9,108.64

4. Answer: 9 years

FV = $ 9,475 / $ 4,740 = 1.9989

( 1 .08 ) ⁿ = 1.9989

n = 9 years