(6) Sean deposits $826 in a savings account that earns interest at Increasing Rates Bank. For the first three years the money is on deposit, the annual effective interest rate is 3%. For the next two years the annual effective interest rate is 4%, and for the following five years the annual effective interest rate is 5%. What is Sean's balance at the end of ten years?

Sean's balance at the end of ten years is $1,245.98.

Explanation:

The formula to compute the amount at the end of n years at r% interest rate is,

Here P = principal amount.

The amount deposited by Sean is, P₀ = $826.

For first n₀ = 3 years the annual effective interest rate is, r₀ = 3%.

⇒

Compute the amount in the bank account after 3 years as follows:

Amount at the end of 3 years is, $902.593.

Now this amount of P₁ = $902.593 is kept in the account at r₁ = 4% for n₁ = 2 years.

⇒

Compute the new amount in the bank account after total 5 years as follows:

Amount at the end of 5 years is, $976.245.

Now this amount of P₂ = $976.245 is kept in the account at r₂ = 5% for n₂₂ = 5 years.

⇒

Compute the new amount in the bank account after total 10 years as follows:

Thus, Sean's balance at the end of ten years is $1,245.98.

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