Question

PLEASE SHOW WORK AND CALCULATE WITH FORMULAS OR EXPLANATION!! THANK YOU SO MUCH. ( please write the formula first so i know the appropriate formula to use thanks!)

What is the value in the year 2040 of an $800 a year annuity with the first payment in 2023 and final payment in 2039. The interest rate is 7% p.a. Please show me the line too.

Answer 1

Information Provided -

Annual Payment = $ 800

First Payment on 1/1/2023

Last Payment on 1/1/2039

Thus, Total Number payment(n) = 17

Interest rate (i) = 7%

To calculate the value of annuity on 1/1/2040 , use following formula -

Future value of Annuity = Annual Payments * FVIAF(i,n)

where,

FVIAF = Future value interest annuity factor

And,

FVIAF(i,n) = [(1+i)(1-(1+i)ⁿ] / - i

FVIAF(7%,17) = [(1+0.07)(1-(1+0.07)¹⁷] / - 0.07

= [1.07(1 - 3.15881521096)]/-0.07

= [1.07*( - 2.15881521096)]/-0.07

= - 2.30993227573 / -0.07

= 32.9990325104

Thus,

Value of Annuity = 800*32.9990325104

= 26,399.2260083

Value of Annuity on 1/1/2040 is $ 26,400 (rounded to nearest dollar)

Please note - Use "=FV(0.07,17,-800,,1)" formula in MS-EXCEL to get the annuity value on 1/1/2040.

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.