Question

Problem 5-3 Compound Interest (LO1) Suppose that the value of an investment in the stock market has increased at an average compound rate of about 5% since 1910. It is now 2016. a. If someone invested $1,000 in 1910, how much would that investment be worth today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. If an investment from 1910 has grown to $1 million, how much was invested in 1910? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Amount Invested in 1910 = $ 1000

Average Compound Rate = 5% per annum

No. of Years investment being kept until 2016 = 106 years

a). Calculating the Future Value or Investment worth today:-

Future Value = Invested Amount(1+Interest Rate)^{Time Period}

= 1000(1+0.05)¹⁰⁶

= $ 176224.26

b). Invested grown to or Future Value of Investment = $ 1000,000

Calculating the amount invested initially:-

Future Value = Invested Amount(1+Interest Rate)^{Time Period}

1000,000 = Invested Amount(1+0.05)¹⁰⁶

Invested Amount = 1000,000/176.2242624

Invested Amount = $ 5674.59

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