MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

Answer:The future value of annuity is $27850302.48The Investment amount is $ 37900.259The compound interest is $ 662799.741 Step-by-step explanation:Given as :The due amount = $ 700700the rate of interest compounded semiannually = 88%The time period = 4 yearsLet The investment principal = $ PThe interest = CILet The future value of annuity = FVNow, The future value of Annuity methodFV = Amount × [tex]\frac{(1+\frac{Rate}{2\times 100})^{2\times time}- 1}{\frac{Rate}{2\times100 }}[/tex]Or, FV = $700700 × [tex]\frac{(1+\frac{88}{2\times 100})^{2\times 4}- 1}{\frac{88}{2\times100 }}[/tex]Or, FV = $700700 × [tex]\frac{(1.44)^{8}-1}{0.44}[/tex]Or, FV = $700700 × 39.7464∴ FV = $27850302.48Now, from compounded methodAmount = Principal × [tex](1+\frac{Rate}{2\times 100})^{2\times Time}[/tex]Or, $ 700700 = P × [tex](1+\frac{88}{2\times 100})^{2\times 4}[/tex]Or, $ 700700 = P × [tex](1.44)^{8}[/tex]or, $ 700700 = P × 18.488∴ P = [tex]\frac{700700}{18.488}[/tex] = $ 37900.259So, Investment amount = $ 37900.259Now, Compound Interest = Amount - PrincipalOr, CI = $ 700700 - $ 37900.259Or, CI = $ 662799.741Hence The future value of annuity is $27850302.48The Investment amount is $ 37900.259The compound interest is $ 662799.741 Answer