1) How long would it take an investment to double under each of the following co

Question

1) How long would it take an investment to double under each of the following conditions? (a) Interest is 3.2% compounded monthly. (Round your answer to three decimal places.) (b) Interest is 5% compounded continuously. (Round your answer to three decimal places.) 2) How much money would you have to invest today at 6% APR compounded monthly to accumulate the sum of $150,000 in 25 years? (Round your answer to two decimal places.) 3) In March 2009, the Bill and Melinda Gates Foundation granted $76 million to AED to fund the Alive and Thrive Initiative. In 2009, Bill Gates, the cofounder and former CEO of Microsoft, had an estimated net worth of $56 billion. How long does it take $56 billion invested at an effective rate of 6.1% to earn $76 million? (Round your numerical answer to four decimal places.)

Explanation / Answer

1

a) 2 = 1 * ( 1 + 0.032 / 12 ) ^x

so taking log on both sides..

x ln ( 1 + 0.032/12 ) = ln 2

x = 260.277 months = 21.690 years

b)

2 = e^(0.05 * t )

so t = 13.863 years

2)

150000 = P * [ 1 + ( 0.06 / 12 ) ] ^ (25* 12)

so P = $ 33,594.85

3) 76 = 56 * ( 1 + 0.061)^n

taking log on both sides

n * ln ( 1.061) = ln( 76/56)

so number of years = n = 5.15744 years

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