12. Problem 5.12
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EFFECTIVE RATE OF INTEREST
Find the interest rates earned on each of the following. Round each answer to two decimal places.
You borrow $700 and promise to pay back $728 at the end of 1 year.
%
You lend $700 and the borrower promises to pay you $728 at the end
of 1 year.
%
You borrow $78,000 and promise to pay back $137,463 at the end of 5
years.
%
You borrow $20,000 and promise to make payments of $6,687.60 at the
end of each year for 5 years.
%
a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
728=700*(1+r/100)^1
(728/700)^1=(1+r/100)
(1+r/100)=1.04
r=1.04-1
=4%
b.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
728=700*(1+r/100)^1
(728/700)^1=(1+r/100)
(1+r/100)=1.04
r=1.04-1
=4%
c.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
137463=78000*(1+r/100)^5
(137463/78000)^(1/5)=(1+r/100)
(1+r/100)=1.12
r=1.12-1
=12%(Approx).
d.Let interest rate be x%
At this rate;present value of payments=20000
20000=6,687.60/1.0x+6,687.60/1.0x^2+..............+6,687.60/1.0x^5
Hence x=interest rate=20%(Approx).
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