Question

Problem 1:

A. Calculate the PV of $100 due in 5 years compounded monthly at 12%.
B. Calculate the FV of $1000 due in 3 years at 6%.
C. Calculate the FVA of $30 due at the end of each of the next 5 years at 4%.
D. Calculate the PVA of $30 due at the end of each of the next 5 years at 4%

Answer 1

For solving question (A) and question (B) we can use the formula of compounding amount.

A=P[1+r]^n

where A= compounded amount(or future value)

P= Principal (or present value)

r= rate of interest per period

n=number of compounding periods.

Answers:

(A) rate(r) shall be 12/12=1%

periods(n) shall be 5*12=60

100=P(1+.01)^60

P=100/(1.01)^60

= 55.04496

(B) FV = 1000(1.06)^3

=1191.016

(C) Future value of annuity= Annuity amount*FVA Factor

FVA factor=(1+r)ⁿ-1/r

=(1+.04)⁵-1/.04

=5.4163

Hence FV of annuity=5.416323*30

=162.49(approx)

(D) Present vlaue of annuity= Annuity amount*PVA Factor

PVA Factor=(1+r)ⁿ-1/(1+r)ⁿ*r

=(1+.04)⁵-1/(1+.04)⁵*.04

=4.451822

PV of annuity=4.451822*30

=133.555(approx)

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