The following situations involve the application of the time value of money conc

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.