Question

Sally makes deposits into a retirement account every year from the age of 30 until she retires at age 65. ​a) If Sally deposits $ 1100$1100 per year and the account earns interest at a rate of 9 %9% per​ year, compounded​ annually, how much does she have in the account when she​ retires? ​b) How much of that total amount is from​ Sally's deposits? How much is​ interest?

Answer 1

a)

Balance of account at retirement = $237,281.83

b)

Total Deposited amount = $38,500

Interest Amount = $198,781.83

Step-by-step explanation:

A fix periodic payments for the specific period of time is the annuity payment. Deposit of $1,100 per year in retirement account is annuity payment.

a)

We can calculate the balance of account on retirement by using following formula

Future Value of Annuity = P x ( 1 + r )^n - 1 / r

Where

P = Periodic payments = $1,100

r = 9%

n = 65 years - 30 years = 35 years

Placing values in the formula

Balance of account at retirement = $1,100 X ( 1 + 9% )^35 - 1 / 9%

Balance of account at retirement = $237,281.83

b)

Total Deposited amount = $1,100 x 35 = $38,500

Interest Amount = Balance of account at retirement - Total Deposited amount = $237,281.83 - $38,500 = $198,781.83