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At a certain interest rate compounded quarterly, Php 10,000.00 will amount to...

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dylzzz | Student, Undergraduate | Honors

Posted July 11, 2013 at 3:39 PM via web

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At a certain interest rate compounded quarterly, Php 10,000.00 will amount to Php45,000.00 in 15 years. What is the corresponding amount at the end of 10 years?

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aruv | High School Teacher | Valedictorian

Posted July 11, 2013 at 4:02 PM (Answer #1)

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Principal P= Php  10000

Amount (in 15 years) A= 45000

conversion period =1/4 year

Time= 15 years

Rate of interest per anuum= R   ( say)

rate of interest quaterly= R/4

We have

A=P(1+(R/4)/100)^(15/(1/4))

A=P(1+R/(400))^60

45000=10000(1+R/400)^60

4.5=(1+R/400)^60

1+R/400= (4.5)^(1/60)

Amount X  (say) after 10 yeras.

X=10000(1+R/400)^(10/(1/4))

X=10000(1+R/400)^40

X=10000 {4.5^(1/60)}^40

X=10000 (4.5)^(40/60)

X=10000 (4.5)^(2/3)

X=10000 x 2.725681

X=27256.8 Php

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