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Hillier Hillier
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Posts: 550
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4 years ago
Silva is contemplating to buy a 20 year annuity paying $2500 at the end of each month. What amount will be required to purchase the annuity, if the annuity provides a return of 6.75% compounded annually?
A) $334 000
B) $47 246
C) $600 000
D) $37 037
E) $567 436
Textbook 

Contemporary Business Mathematics with Canadian Applications


Edition: 11th
Authors:
Read 128 times
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AxyAxy
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Posts: 348
4 years ago
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wrote...
3 years ago
Correct, thank you
wrote...
A month ago
Given about an annuity,

Monthly payment PMT = $2500

term period t = 20 years

interest rate EAR = 6.75% compounded annually

First we need to calculated monthly rate.

So, Monthly rate r = ((1+EAR)^(1/12)) - 1 = ((1.0675^(1/12)) - 1) = 0.5458%

So, price of the annuity is calculated using PV formula of ordinary annuity

PV = PMT*(1 - (1+r)^(-n*t))/r

where r = 12 months in a year

So, price of the annuity = 2500*(1 - (1 + 0.005458)^(-12*20))/0.005458 = $333998.96
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