# Present Value and EAR

Find the future vales of the following ordinary annuities:

a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12 %, compounded semiannually.

b: FV of $200 paid each 3 months for 5 years at a nominal rate of 12%, compounded quarterly

c. These annuities receive the same amount of cash during the 5- year period and earn interest at the same nominal rate, yet the annuity inpart b ends up larger than one in part a, Why does this occur?

Effective versus nominal interest rate Bank A pays 4 % interest, compounded annually, on deposits, while Bank B pays 3.5 percent, compound daily

a. Based on the EAR or (EFF% which bank should you use?

b.Could the choice of bank influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest?

Please show calculations.

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#### Solution Preview

Please find my response below with all the calculations. I have used a financial calculator to do all the calculations.

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a)

Payment amount (PMT) = 400

Nominal Rate per annum = 12%

So rate for every 6 months = 12/2 = 6%

Number of periods = 5 times 2 = 10

Putting these values in the calculator and solving for Future Value we get :

FV = 5,272,318

If you want to use excel, you will put the following formula in the ...

#### Solution Summary

The solution calculates future values of amounts in the first part and then calculated the effective annual rates for scenarios in the second part. Full detailed explanation has been given for every part of the question.