Question

Suppose you invest $10,145.00 into an account earning an interest rate of 2.197% compounded continuously for 1 year(s) and thereafter earning an interest rate of 3.252% compounded quarterly. How much money is in the account after 9 years?

Answer 1

The amount of money in the account after 9 years is $13,918.09.

Step-by-step explanation:

To calculate the amount of money in the account after 9 years, we can use the formula for compound interest:

A = P * e^(rt)

Where:

• A is the final amount in the account
• P is the initial amount invested
• r is the interest rate
• t is the time in years
• e is the constant approximately equal to 2.71828

For the first year, the interest rate is 2.197% and the time is 1 year, so we have:

A = 10145 * e^(0.02197 * 1) = $10,358.84

For the remaining 8 years, the interest rate is 3.252% compounded quarterly. The interest rate per quarter is 3.252 / 4 = 0.813%. The time in quarters is 8 * 4 = 32 quarters. So we have:

A = 10358.84 * (1 + 0.00813)^(32) = $13,918.09

Therefore, the amount of money in the account after 9 years is $13,918.09.