MATH SOLVE

5 months ago

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 = [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.......