Q:

# 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

A:
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     =  $$\text{Principal} \times [1 +\frac{Rate}{100}]^{\text{Number of years}}$$ = $$200 \times [1 + \frac{2}{100}]^n$$ where n= 1,2,3.......