Question

Stanford Simmons, who recently sold his Porsche, placed $10,000 in a savings account paying annual compound interest of 6%. A.) Calculate the amount of money that will have accrued if he leaves the money in the bank for 1, 5, and 15 years. B.) If he moves his money into an account that pays 8% or one that pays 10%, rework part (a) using these new interest rates. C.) What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem?

Answer 1

A.) For 1 year: $10,600, 5 years: $13,382.16, 15 years: $21,913.02. B.) At 8% for 1 year: $10,800, 5 years: $14,693.28, 15 years: $32,071.89. At 10% for 1 year: $11,000, 5 years: $16,105.10, 15 years: $41,772.73. C.) Higher interest rates and longer time periods lead to larger future sums.

Step-by-step explanation:

To calculate the amount of money that will have accrued if Stanford leaves the money in the bank for 1, 5, and 15 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

For 1 year: A = 10000 * (1 + 0.06/1)^(1*1) = $10,600
For 5 years: A = 10000 * (1 + 0.06/1)^(1*5) = $13,382.16
For 15 years: A = 10000 * (1 + 0.06/1)^(1*15) = $21,913.02