Answer to Question #261602 in Financial Math for chitta

Question

Alternatively, you can deposit a fixed payment of R 30,000 from your monthly salary

into the HBL savings account every month for the five years. The savings account pays

an annual interest rate of 11.25%, compounded monthly. How much will you be able to

accumulate at the end of sevene years?

Answer 1

Pn=d{(1 + r/k)^Nk -1}/(r/k)

Whereby:

-P_N is the balance in the account after N years.

-d is the regular deposit (the amount you deposit each year, each month, etc.)

-r is the annual interest rate in decimal form.

-k is the number of compounding periods in one year.

Thus,

Pn = 30000{(1 + 0.1125/12)⁶⁰ - 1}/(0.1125/12)

=30000{(1 + 0.0094)⁶⁰ - 1}/(0.0094)

=30000(0.7531)/(0.0094)

22591.95/0.0094

=2403398.997

Accumulation at the end of seven years=

2403398.997 = d{(1 + 0.1125/12)⁸⁴ - 1}/(0.1125/12)

d{(1 + 0.0094)⁸⁴ - 1}/(0.0094)

1.1944d/0.0094 = 2403398.997

1.1944d = 2403398.997*0.0094

1.1944d = 22591.95

=R 189148.95