The following situations involve the application of the time value of money conc
ID: 2443247 • Letter: T
Question
The following situations involve the application of the time value of money concept:
Janelle Carter deposited $9,750 in the bank on January 1, 1993, at an interest rate of 11% compounded annually. How much has accumulated in the account by January 1, 2010?
Mike Smith deposited $21,600 in the bank on January 1, 2000. On January 2, 2010, this deposit has accumulated to $42,487. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit?
Lee Spony made a deposit in the bank on January 1, 2003. The bank pays interest at the rate of 8% compounded annually. On January 1, 2010, the deposit has accumulated to $15,000. How much did Lee originally deposit on January 1, 2003?
Nancy Holmes deposited $5,800 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 $15,026. How many years has the deposit been invested?
Explanation / Answer
1. Janelle Carter deposited $9,750 in the bank on January 1, 1993, at an interest rate of 11% compounded annually. How much has accumulated in the account by January 1, 2010?
Answer: $ 63799.64
Here,
Present value of deposit is $9,750
Rate of interest is 11%
Period is 18 years (1-Jan 1993 to 1-Jan 2010)
Future value = $63799.64.
This can be found using the below formula:
FV= PV*(1+i)n
= 9750*(1+.11)18 = 63799.64
Using a financial calculator input values as below:
PV= -9750
I/YR = 11
N = 18
Compute value for FV
2. Mike Smith deposited $21,600 in the bank on January 1, 2000. On January 2, 2010, this deposit has accumulated to $42,487. Interest is compounded annually on the account. What rate of interest did Mike earn on the deposit?
Answer: 6.99%
Here,
Present value of deposit is $21,600
Period is 10 years (1-Jan 2000 to 2-Jan 2010)
Future value = $42487
The same formula can be used, this time solving for ‘i’:
FV= PV*(1+i)n
42487 = 21600*(1+i)10
i=6.99%
Using a financial calculator input values as below:
PV= -21600
FV = 42487
N = 10
Compute value for I/YR
3. Lee Spony made a deposit in the bank on January 1, 2003. The bank pays interest at the rate of 8% compounded annually. On January 1, 2010, the deposit has accumulated to $15,000. How much did Lee originally deposit on January 1, 2003?
Answer: $ 8752.35
Here,
Future value of deposit is $15,000
Rate of interest is 8%
Period is 7 years (1-Jan 2003 to 1-Jan 2010)
This can be found using the below formula:
PV= FV/(1+i)n
PV = 15000/(1+.08)7 = 8752.35
Using a financial calculator input values as below:
FV= 15000
I/YR = 8
N = 7
Compute value for PV
4. Nancy Holmes deposited $5,800 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 $15,026. How many years has the deposit been invested?
Answer: 9.98 years
Here,
Present value of deposit is $5,800
Rate of interest is 10%
Future value = $15,026
This can be found using the below formula:
FV= PV*(1+i)n and solving for ‘n’
15026 = 5800*(1+.10)n = 9.98
Using a financial calculator input values as below:
PV= -5800
FV = 15026
I/YR = 10
Compute value for N