Question

Find the future value of an annuity due of ​$700700 semiannually for fourfour years at 88​% annual interest compounded semiannually. What is the total​ investment? What is the​ interest?

Answer 1

The future value of annuity is $27850302.48

The Investment amount is $ 37900.259

The compound interest is $ 662799.741

Explanation:

Given as :

The due amount = $ 700700

the rate of interest compounded semiannually = 88%

The time period = 4 years

Let The investment principal = $ P

The interest = CI

Let The future value of annuity = FV

Now, The future value of Annuity method

FV = Amount ×
`((1+(Rate)/(2* 100))^(2* time)- 1)/((Rate)/(2*100 ))`

Or, FV = $700700 ×
`((1+(88)/(2* 100))^(2* 4)- 1)/((88)/(2*100 ))`

Or, FV = $700700 ×
`((1.44)^(8)-1)/(0.44)`

Or, FV = $700700 × 39.7464

∴ FV = $27850302.48

Now, from compounded method

Amount = Principal ×
`(1+(Rate)/(2* 100))^(2* Time)`

Or, $ 700700 = P ×
`(1+(88)/(2* 100))^(2* 4)`

Or, $ 700700 = P ×
`(1.44)^(8)`

or, $ 700700 = P × 18.488

∴ P =
`(700700)/(18.488)` = $ 37900.259

So, Investment amount = $ 37900.259

Now,

Compound Interest = Amount - Principal

Or, CI = $ 700700 - $ 37900.259

Or, CI = $ 662799.741

Hence The future value of annuity is $27850302.48

The Investment amount is $ 37900.259

The compound interest is $ 662799.741 Answer