Question

Suppose that the value of an investment in the stock market has increased at an average compound rate of about 5% since 1912. It is now 2016.

a. If someone invested $1,000 in 1912, 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 1912 has grown to $1 million, how much was invested in 1912?

Old Time Savings Bank pays 3% interest on its savings accounts. If you deposit $3,000 in the bank and leave it there: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. How much interest will you earn in the first year?

b. How much interest will you earn in the second year?

c. How much interest will you earn in the 10th year?

Answer 1

a. Value of Investment today = 1000 * (1 + Interest)^Years

Value of Investment today = 1000 * (1.05)^105

Value of Investment today = 1000 * 167.833

Value of Investment today = $167832.63

b. If an investment from 1912 has grown to $1 million, how much was invested in 1912?

Value of Investment today = 1000 * (1 + Interest)^Years

1000000 = 1000 * (1 + Interest)^105

1000 = (1 + Interest)^105

Interest = 6.80%

c. Old Time Savings Bank pays 3% interest on its savings accounts. If you deposit $3,000 in the bank and leave it there: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. How much interest will you earn in the first year? 3000 * 3% = $90

b. How much interest will you earn in the second year? 3090 * 3% = $92.70

c. How much interest will you earn in the 10th year? 3000 * (1.03^10 - 103^9) = $117.43