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

recursive formula represents the total amount of money in the bank is given by
`a_(n+1)=a_n(1.02)^n+15`

Explanation:

Given : 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.

We have to write a recursive formula representing the total amount of money in the bank.

Since, she has $200 in her account so first term is 200

`a_0=200`

and At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance.

balance at beginning of year 1 = 200+15=215

`a_1=215`

at the beginning of year 1 she has balance = 215 + interest on 215 + 15

`(1+(r)/(100))^n` , where n is time period.

r = 2%

`(1+(2)/(100))^n=(1.02)^n`

Thus, at the beginning of year 1 she has balance =
`a_2=215(1.02)+15`

So at every next year she will have interest on previous balance + $15

So , recursive formula represents the total amount of money in the bank is given by
`a_(n+1)=a_n(1.02)^n+15`