Question

Kim Wilson deposits 40, 000 dollars in an IRA at 2% interest compounded continuously for her retirement in 20 years. She intends to make continuous deposit at the rate of 1, 200 dollars a year until she retires. How much will she has accumulated at that time?

Answer 1

Step 1:

Kim Wilson deposits the amount is .

The rate of interest is .

The time perid is .

The amount is compounded continuously.

Formula for amount of continuously compounding : .

.

Step 2:

She intends to make continuous deposit is .

The time period is .

The annuity formula is .

Where is the balance in the account after years, is the regular deposit,

is the annual interest and is the compounding period in one year.

.

.

The total amount accumulated is .

.

She accumulated the amount at retirement time is .

Solution:

She accumulated the amount at retirement time is .