# Case 1

**Topics:**Compound interest, Time value of money, Nominal interest rate

**Pages:**8 (2168 words)

**Published:**March 17, 2013

A. The future value of a $10,000 CD that has a maturity of 1 year at maturity with 10% interest is $11,000. Financial Calculator Inputs: $ -10,000=PV, 1=N, I=10, FV=? ($11,000) B. The future value of a 1-year, $10,000 CD after one year at an interest rate of 5.0% is $10,500. Financial Calculator Inputs: $-10,000=PV, 1=N, 5=I, FV=? ($10,500) The future value of a 1-year, $10,000 CD after one year at an interest rate of 15.0% is $11,500. Financial Calculator Inputs: $-10,000=PV, 1-N, 15=I, FV=? ($11,500) C. The effective annual rate of First National Bank’s CD offering a 10% nominal interest rate compounded semiannually is 10.25%.

Calculations: (1+.10/2)^2 -1 =.1025

The future value of a $10,000 dollar CD compounded semiannually for one year at The First National Bank is $11,025 Calculations: FV=$10,000(1.1025) FV=$11,025

D. Using a 360 day bankers year, the Effective Annual Rate of Pacific Trust’s

10% interest CD compounded daily is 10.52%

Calculations: (1+.10/365)^365 –1 =.1052

The future value of Pacific Trust’s $10,000 CD with an effective annual rate Of 10.52% after one year is $11,052.

Financial Calculator Inputs: $ -10,000=PV, 1=N, 10.52=I, FV=? ($11,052)

First National Bank would have to offer a nominal rate of 10.26% on it’s

Semiannually compounded CD to be competitive with Pacific Trust’s daily compounding CD.

Calculations: $10,000(1+X/2)^2 = $11,052”FV of Pacific Trust’s CD”

(1+X/2)^2 = 1.052

(Take square root of both sides of equation)

(1+X/2) =1 .0513-(1) (

X/2=.0513(*2) ( X=.1026

2. Considering a 5-Year CD, rework parts a-d of question 1

A. The value at maturity of a $10,000 CD with a 10% interest rate is $16,105.10 Inputs: $-10,000=PV, 5=N, 10=I, FV-? ($16,105.10)

B. The future value of a 5-year, $10,000 CD after five years at an interest rate of 5.0% is $12,762.82. Financial Calculator Inputs: $-10,000=PV, 5=N, 5=I, FV=? ($12,762.82)

The future value of a 5-year, $10,000 CD after five years at an interest rate of 15.0% is $20,133.57. Financial Calculator Inputs: $-10,000=PV, 5-N, 15=I, FV=? ($20,113.57) C. The effective annual rate of First National Bank’s CD offering a 10% nominal interest rate compounded semiannually is 10.25%.

Calculations: (1+.10/2)^2 -1 =.1025

The future value of a $10,000 dollar CD compounded semiannually for five years at The First National Bank is $16,288.95

Calculations: FV=$10,000(1.1025)^5 FV=$16,288.95

D. Using a 360 day bankers year, the Effective Annual Rate of Pacific Trust’s

10% interest CD compounded daily is 10.52%

Calculations: (1+.10/365)^365 –1 =.1052

The future value of Pacific Trust’s $10,000 CD with an effective annual rate Of 10.52% after five years is $16,489.38.

Financial Calculator Inputs: $-10,000=PV, 5=N, 10.52=I, FV=?($16,489.38)

3. It is estimated that in 5 years the total cost for one year of college will be $20,000

A. $12,418.43 must be invested today in a CD paying 10% annual interest rate in order to accumulate the needed $20,000 for college in five years. Financial Calculator Inputs: $20,000=FV, 5=N, 10=I, PV=? ($-12418.43) B. If only $10,000 is invested today for 5 years, an interest rate of 14.87% is required to reach the goal of $20,000 in 5 years for college tuition. Financial Calculator Inputs: $-10,000=PV, 5=N, $20,000=FV, I=? (14.8698)

If only $10,000 is invested, the First National Bank must offer a stated rate of

14.35% on its semiannually compounded CD to accumulate...

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