Respuesta :
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 × [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 = $27850302.48
Now, from compounded method
Amount = 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] = $ 37900.259
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
