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 $9,790 in the bank on January 1, 2000, at an interest rate of 12% compounded annually. How much has accumulated in the account by January 1, 2017? Round to the nearest whole dollar.
$

2. Mike Smith deposited $21,410 in the bank on January 1, 2007. On January 2, 2017, this deposit has accumulated to $42,117. 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 7% compounded annually. On January 1, 2017, the deposit has accumulated to $12,070. How much money did Lee originally deposit on January1, 2010? Round to the nearest whole dollar.
$

4. Nancy Holmes deposited $6,930 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 $12,827. How many years has the deposit been invested? Round to the nearest whole year.
years

Answer 1

Solution

Question 1

Amount Deposited (P) = $9,790
Rate of Interest (r) = 12%
Term (n) = January 1, 2000 to January 1, 2017, i.e. 16 Years, or 16

Now, Amount Accumulated in January 1, 2017 = P * (FVIF_12%,16)
= 9790 * (FVIF_12%,16)
= 9790 * 6.130
= 60013 (Approx.)

Answer: Amount Accumulated in January 1, 2017 will be $60013

Question 2

Amount Deposited on January 1, 2007 (P) = $21,410
Amount Accumulated on January 2, 2017 (F) = $42,117
Term (n) = 10

Therefore, it is as follows,
21410 * (FVIF_r,10) = 42117
Or, (FVIF_r,10) = 42117 / 21410
Or, (FVIF_r,10) = 1.967 (Approx.)

Now, under FV table (FV of $1), at 7%, Future Value will be 1.967 approximately.

Answer: Rate of Interest earned will be 7%

Question 3

Amount Accumulated on January 1, 2017 (F) = $12,070
Rate of Interest (r) = 7%
Term (n) = January 1, 2010 to January 1, 2017, i.e. 6

Therefore, Money originally deposited on January1, 2010 (P) = F * (PVIF_7%,6)
= 12070 * (PVIF_7%,6)
= 12070 * 0.666
= 8039

Answer: $8039 was originally deposited on January1, 2010

Question 4

Amount Deposited = $6,930
Present Value of Deposit (P) = $12,827
Rate of Interest (r) = 8%

Therefore, it is as follows,
12827 * (FVIF_8%,n) = 6930
Or, (FVIF_8%,n) = 6930 / 12827
Or, (FVIF_8%,n) = 0.540 (Approx.)

Now, under PV table (PV of $1), at n = 8, Present Value will be 0.540 approximately.

Answer: For 8 years the deposit has been invested