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 $9,510 in the bank on January 1, 2000, at an interest rate of 10% compounded annually. How much has accumulated in the account by January 1, 2017? Round to the nearest whole dollar. $ 52,875 2. Mike Smith deposited $22,540 in the bank on January 1, 2007. On January 2, 2017, this deposit has accumulated to $48,662. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit? Round to the nearest whole percent. 8 % 3. Lee Spony made a deposit in the bank on January 1, 2010. The bank pays interest at the rate of 5% compounded annually. On January 1, 2017 , the deposit has accumulated to $15,630. How much money did Lee originally deposit on January1, 2010? Round to the nearest whole dollar. $ 10,579

Answer 1

Q#1:

Given,

Money deposited (P) = $9,510

Period of deposit= 17 years

Interest rate= 10%

Amount accumulated by January 1, 2017 = P*(FVIF 10%, 17)

=9510* 5.054470 = $48,068

Q#2:

Given,

Money deposited (P) = $22,540

Future Value (F) = $48,662

Period of deposit= 10 years

F/P= 2.158917

As per FVIF table, the interest rate for 10 years nearest to this factor is 8%

Therefore, interest rate= 8%

Q#3:

Future Value (F) = $15,630

Period of deposit= 7 years

Interest rate= 5%

Amount deposited= F*(PVIF 5%, 7)

As per PVIF table, PVIF 5%, 7 = 0.710681

Therefore, amount deposited= $11,108