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Suppose the interest rate is 9% APR with monthly compounding
Suppose the interest rate is 9% APR with monthly compounding. Then the present value of
an annuity that pays $250 every three months for the next five years is closest to:
A) $2,280
B) $3,985
C) $3,990
D) $3,995
Expert Solution
Computation of the present value of annuity:-
Correct option is B). $3,985
PV of annuity = Annuity*((1-1/(1+rate)^n)/rate)
Here,
Rate 2.27% (quarterly)
n = 5*4 = 20 periods (quarterly)
PV of annuity = $250*((1-1/(1+2.27%)^20)/2.27%)
= $250*15.93796
= $3,984.50 Or $3,985
Working note:-
EAR = (1+APR/n)^n-1
= (1+9%/12)^12-1
= 1.0938 - 1
= 9.38%
EAR = (1+APR/n)^n-1
9.38% = (1+APR/4)^4-1
(1+APR/4) = (1+9.38%)^(1/4)
APR/4 = 1.0227 - 1
APR = 2.27% * 4
= 9.07%
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