Question

Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each month for 9 months in a fund that gives 5% per annum compounded monthly. How much would the value of her savings be after 7 months?

Answer 1

The rate is r = 5% = 0.05
Compounding interval, n = 12, monthly compounding
Therefore
r/n = 0.05/12 = 0.004167

The first deposit has a duration of 7 months. Its value is
a₁ = 1000*(1.004167)⁷

The second deposit has a duration of 6 months. Its value is
a₂ = 1000*(1.004167)⁶
and so on.

The values after each month from a geometric sequence with
a = 1000*(1.004167)
r = 1.004167

Over 7 months, the total sum is
$\frac{1000*1.004167*(1-1.004167^{7} )}{1-1.004167} =7117.64$


Answer: Php 7,117.64