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?

After 7 months her savings will be 7117.64.

Step-by-step explanation:

Given :

Rate is r = 5% = 0.05

Compounding interval, n = 12

Solution :

Now,

[tex]\rm \dfrac{r}{n} = \dfarc{0.05}{12}[/tex]

[tex]\rm \dfrac{r}{n} = 0.004167[/tex]

Now first deposit duration is 7 months. Therefore, its value is  [tex]\rm a_1 = 1000\times (1.004167)^7[/tex]

Now second deposit duration is 6 months. Therefore, its value is

[tex]\rm a_2 = 1000\times (1.004167)^6[/tex]

Now third deposit duration is 5 months. Therefore, its value is

[tex]\rm a_3 = 1000\times (1.004167)^5[/tex]

and so on.

The values are in geometric sequence where

[tex]\rm a = 1000\times (1.004167)[/tex]

[tex]\rm r = 1.004167[/tex]

We know that the sum of the geometric sequence is given by,

[tex]\rm S_n = \dfrac{a (r^n-1)}{(r-1)}[/tex]    ------ (1)

Now put the values of a and r in equation (1),

[tex]\rm S_7=\dfrac{1000\times(1.004167)((1.004167)^7-1)}{(1.004167-1)}[/tex]

[tex]\rm S_7 = 7117.64[/tex]

After 7 months her savings will be 7117.64.

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