Problem

A savings account typically accrues savings using compound interest. If you deposit $1,000 with a 10% interest rate per year, after one year you will have $1,100. If you leave this money in the account for another year at 10% interest, you will have $1,210. After three years you will have $1,331, and so on. Write a program that inputs the initial amount, an interest rate per year, and the number of years the money will accrue compound interest. Write a recursive function that calculates the amount of money that will be in the savings account using the input information. To verify your function, the amount should be equal to P(1+i)n, where P is the amount initially saved i is the interest rate per year, and n is the number of years.