# Problem with saving account

• Apr 3rd 2007, 11:21 PM
Mariana
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?
• Apr 4th 2007, 07:11 AM
Soroban
Hello, Mariana!

These involve an Annuity and then Compound Interest.

Quote:

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

Quote:

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

Quote:

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.