5A-5 CONTINUOUS COMPOUNDING You have the choice of placing your savings in an ac

Question

5A-5

CONTINUOUS COMPOUNDING You have the choice of placing your savings in an account paying 10.25% compounded annually, an account paying 10.1% compounded semiannually, or an account paying 9.5% compounded continuously. To maximize your return, which would you choose?

5A-6

CONTINUOUS COMPOUNDING You have $11,572.28 in an account that has been paying an annual rate of 9%, compounded continuously. If you deposited some funds 15 years ago, how much was your original deposit?

5A-7

CONTINUOUS COMPOUNDING For a 10-year deposit, what annual rate payable semiannually will produce the same effective rate as 3% compounded continuously?

5A-8

PAYMENT AND CONTINUOUS COMPOUNDING You place $2,000 in an account that pays 8% interest compounded continuously. You plan to hold the account exactly 3 years. At the same time, in another account you deposit money that earns 9% compounded semiannually. If the accounts are to have the same amount at the end of the 3 years, how much of an initial deposit do you need to make now in the account that pays 9% interest compounded semiannually?

Explanation / Answer

5A-5

First account pay 10.25% compounded annually. So effective annual rate is 10.25%.

Second account pays 10.01% Compounded semiannually.

So, effective annual rate = [(1 + 10.10% / 2) ^ 2] - 1

= 1.1036 - 1

= 10.36%

Effective annual rate for semiannual comounded rate is 10.36%.

Third account pays 9.50% compounded continuously.

So, effective annual rate = [2.718 ^ (9.50% × 1)] - 1

= 1.0996 - 1

= 9.96%

So, effective annual rate for continuously compounded is 9.96%.

Since, Effective annual rate for compounded semiannually is highest among all three options. So an save in account in which interest compounded semiannually.

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