Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance. Which recursive formula represents the total amount of money in the bank?

Accepted Solution

Amount of money that Victoria had in her account at the end of year                                                         = $ 200Money Deposited At each subsequent year = $ 15 Total Balance after a year = $ 200 + $ 15 = $ 215Rate of interest = 2 %As there are two types of interest : 1. Simple Interest 2. Compound InterestIn simple interest Principal doesn't get affected. As rate of interest is applied on Money invested in the beginning.But in compound interest , Principal changes on each day, or month, or semi annually, or yearly the way the interest is applied.So, Recursive Formula that represents the total amount in the bank      = Amount after each subsequent year     =  [tex]\text{Principal} \times [1 +\frac{Rate}{100}]^{\text{Number of years}}[/tex] = [tex]200 \times [1 + \frac{2}{100}]^n[/tex] where n= 1,2,3.......