Question

What lump sum of money must be deposited in a bank account at present time so that Php 500 monthly can be withdrawn for five years with the first withdrawal scheduled six years from today? Interest rate is 9% compounded quarterly.​

Answer 1

Using compound interest, it is found that a sum of $16,586.26 must be deposited.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

In which:

• A(t) is the amount of money after t years.

• P is the principal(the initial sum of money).

• r is the interest rate(as a decimal value).

• n is the number of times that interest is compounded per year.

• t is the time in years for which the money is invested or borrowed.

In this problem:

• We want to have Php 500 to be withdrawn monthly for 5 years, hence A(t) = 500 x 12 x 5 = 30000.

• The first withdraw is 6 years from now, hence t = 6.

• The interest rate is of r = 0.09.

• Compounded quarterly, hence n = 4.

The amount deposited is the principal, hence:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$30000 = P\left(1 + \frac{0.09}{4}\right)^{4(6)}$

$(1.025)^{24}P = 30000$

$P = \frac{30000}{(1.025)^{24}}$

$P = 16586.26$

A sum of $16,586.26 must be deposited.

To learn more about compound interest, you can take a look at brainly.com/question/25781328