Question

If you invest today SR2,500 every year until the end of 20^th year at the rate of interest of 4.5% for the first 15 years and 5% thereafter, what is the value of your investment at the end of 25 years

Answer 1

Interest rate is different for 15 years and next 5 years So we will calculate Future value of 2 different annuities Then combined future value of both annuities will be value of investment at 25th year.

Interest rate is 4.5% for 15 years

Annuity amount = 2500

time (n) of annuity deposits= 15

Future value at end of 15th year = Annuity *(((1+i)^n)-1)/i

2500*(((1+4.5%)^15)-1)/4.5%

=51960.14 (This is value at end of 15th year.)

This amount is held until 25th year.

So time (n) =10

Present value at 15th year = 51960.14

Interest rate (i) = 5%

Future value = Present value *(1+i)^n

51960.14*(1+5%)^10

=84637.59

Now

Annuity for 5 years = 2500

Interest rate = 5%

Time (n) of annuity deposits = 5

Future value at end of 20th year = Annuity *(((1+i)^n)-1)/i

2500*(((1+5%)^5)-1)/5%

=13814.08

(This is value at end of 20h year.)

This amount is held until 25th year.

So time (n) =5

Present value at 20th year = 13814.08

Interest rate (i) = 5%

Future value = Present value *(1+i)^n

13814.08*(1+5%)^5

=17630.66

Combined future value at 25 th year =84637.59+17630.66

102268.25

So value of investment at end of 25th year is $102268.25