MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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

[tex] \frac{1000*1.004167*(1-1.004167^{7} )}{1-1.004167} =7117.64[/tex]

Answer: Php 7,117.64

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

[tex] \frac{1000*1.004167*(1-1.004167^{7} )}{1-1.004167} =7117.64[/tex]

Answer: Php 7,117.64