a.)Use the \"rule of 72\" to estimate the doubling time (in years) for the inter

Question

a.)Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.) 9% compounded annually. "rule of 72" yr exact answer yr

b.)Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.) 15% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 1.3% per month.]

c.)You have just received $185,000 from the estate of a long-lost rich uncle. If you invest all your inheritance in a tax-free bond fund earning 6.2% compounded quarterly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)

d.)You have just won $150,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 6% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)

Explanation / Answer

a. As per the rule of 72, doubling period = 72 / 9 = 8 years.

b. Effective interest rate for monthly compounding = [ 1 + r / 12 ] 12 - 1

where r is the stated rate.

In the given situation, effective interest rate = [ 1 + 0.15 / 12 ] 12 - 1 = 0.16075 or 16.08 %

c. Future Value = $ 1,000,000

Present Value x ( 1 + r/ 4) 4n = $ 1,000,000

or ( 1 + 0.0155) 4n = $ 1,000,000 / $ 185,000 = 5.40541

1.0155 = 5.405411/ 4n

4n is 110 periods

n = 27.5 years.

d. 150,000 ( 1 + 0.06 / 52) 52n = 1,000,000

or 1.0011538 52n = 6.66667

52n = 1646

n = 1646 / 52 = 31.65 years.

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