# Math Help - Problem with saving account

1. ## Problem with saving account

You save 20 000 € on a savings account at the end of each year for 9 years. The annual interest rate is 3%.
a) How much is the total amount immediately after the last deposit?

b) How much is the total amount 5 years after the last deposit?
You save an amount K on a savings account at the end of each year for 9 years.The annual interest rate is 3%.

c) How much is the yearly savings amount if the total amount 5years after the last deposit is 300 000?

2. Hello, Mariana!

These involve an Annuity and then Compound Interest.

You save $20 000 in a savings account at the end of each year for 9 years. The annual interest rate is 3%. a) How much is the total amount immediately after the last deposit? . . . . . . . . . . . . . . . . . . .(1 + i)^n - 1 Annuity formula: . A .= .D --------------- . . . . . . . . . . . . . . . . . . . . . . i where D = periodic deposit . . . . . i = periodic interest rate . . . . .n = number of periods . . . . .A = final amount We have: D = 20,000, i = 0.03, n = 9 . . . . . . . . . . . . . . . . . . 1.03^ 9 - 1 Therefore: . A .= .20,000 ------------- . .$203,182.12
. . . . . . . . . . . . . . . . . . . . 0.03

b) You save an amount K on a savings account at the end of each year for 9 years.
The annual interest rate is 3%.
How much is the total amount 5 years after the last deposit?
We deposit K dollars each year for 9 years at 3%

. . . . . . . . . . . . . . . . . . . . . . 1.03^
9 - 1
At the end of 9 years: . A .= .K ------------- . .10.1591K
. . . . . . . . . . . . . . . . . . . . . . . . 0.03

This amount is left in the account for another 5 years.

. . Its value will be: .10.1581K (1.03)^
5 . .11.776K

c) How much is the yearly savings amount if the total amount 5 years
after the last deposit is $300 000? If the above value is$300,000: .11.776K .= .300,000 . . K . .\$25,475.54

Drat . . . The deposits are made at the end of each year.
Are all my answers wrong?
If they are, would someone correct them . . . please?