Case 1

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• Published : March 17, 2013

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1. Consider a 1-Year \$10,000 CD

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...