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

Answer:

The future value of annuity is $27850302.48

The Investment amount is $ 37900.259

The compound interest is $ 662799.741

Step-by-step 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 × $\frac{(1+\frac{Rate}{2\times 100})^{2\times time}- 1}{\frac{Rate}{2\times100 }}$

Or, FV = $700700  × $\frac{(1+\frac{88}{2\times 100})^{2\times 4}- 1}{\frac{88}{2\times100 }}$

Or, FV = $700700  ×  $\frac{(1.44)^{8}-1}{0.44}$

Or, FV = $700700  × 39.7464

∴   FV = $27850302.48

Now, from compounded method

Amount = Principal × $(1+\frac{Rate}{2\times 100})^{2\times Time}$

Or, $ 700700 =  P  × $(1+\frac{88}{2\times 100})^{2\times 4}$

Or,  $ 700700 =  P  × $(1.44)^{8}$

or, $ 700700 =  P  × 18.488

∴ P  = $\frac{700700}{18.488}$ = $ 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