Question

A bank offers a savings account which pays 3% interest per year. The amount of money in the account after t years is represented by the expression P(1 + I/n)^nt, where P represents the initial amount of money invested, n represents the number of times per year the interest is compounded, i represents the interest rate, and t represents the number of years the money has been invested. Which statement describes what happens with the savings account when the interest is compounded monthly instead of yearly? Select two that apply.

Answer 1

When the interest is compounded monthly instead of yearly, two things happen: the interest rate is higher and the amount of money in the account grows faster over time. This is because the interest is compounded more frequently.

Step-by-step explanation:

When the interest is compounded monthly instead of yearly, two things happen:

1. The interest is compounded more frequently, resulting in more compounding periods per year and a higher effective interest rate.
2. The amount of money in the account grows faster over time because of the increased compounding frequency. This is because the expression P(1 + I/n)^nt calculates the future value of the investment based on the compounding frequency.

For example, if the interest is compounded monthly with an annual interest rate of 3%, the effective interest rate per period would be 3%/12 = 0.25%. This means that every month, the amount of money in the account would increase by 0.25% compared to the previous month.