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. $ 65,296 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. % 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. $ 4. Nancy Holmes deposited $4,760 in the bank on January 1 a few years ago. The bank pays an interest rate of 10% compounded annually, and the deposit is now worth $13,581. How many years has the deposit been invested? Round to the nearest whole year. years

Answer 1

All solved using Future Value Formula as under:

(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.

FV = PV*(1+r)^n
PV = Deposit = $9510
r is rate of interest per year = 10%
n is no. of years = 2000 to 2017 = 18 years
FV = Accumulated Balance in the account by January 1, 2017
FV = 9510*(1+0.10)^18 = $52874.81
FV= $52875

(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.

FV = PV*(1+r)^n
PV = Deposit = $22540
r is rate of interest per year = ?
n is no. of years = 2007 to 2017 = 11 years
FV = $48662
48662 = 22540*(1+r)^11
(1+r)^11 = (48662/22540)
(1+r)^11 = 2.158917
Using trial and error method, r is 7.25%

(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.

FV = PV*(1+r)^n
PV = Deposit = ?
r is rate of interest per year = 5%
n is no. of years = 2010 to 2017 = 8 years
FV = $15630
15630 = PV*(1+5%)^8
PV = 15630/1.47745544
PV = 10578.9993
PV = $10579

(4) Nancy Holmes deposited $4,760 in the bank on January 1 a few years ago. The bank pays an interest rate of 10% compounded annually, and the deposit is now worth $13,581. How many years has the deposit been invested? Round to the nearest whole year.

FV = PV*(1+r)^n
PV = Deposit = $4760
r is rate of interest per year = 10%
n is no. of years = ?
FV = $13581
13581= 4760*(1+0.10)^n
(1+0.10)^n = 13581/4760
(1.10)^n = 2.85315126
Using trial and error method, n = 11 years.