Question

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?

Answer 1

Amount of money that Victoria had in her account at the end of year

= $ 200

Money Deposited At each subsequent year = $ 15

Total Balance after a year = $ 200 + $ 15 = $ 215

Rate of interest = 2 %

As there are two types of interest : 1. Simple Interest 2. Compound Interest

In 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} * [1 +(Rate)/(100)]^{\text{Number of years}}`

=
`200 * [1 + (2)/(100)]^n` where n= 1,2,3.......