Effective rate of interest Find the interest rates earned on each of the followi

Question

Effective rate of interest

Find the interest rates earned on each of the following. Round each answer to two decimal places.

a. You borrow $700 and promise to pay back $791 at the end of 1 year.

_______%

b. You lend $700 and the borrower promises to pay you $791 at the end of 1 year.

_______ %

c. You borrow $70,000 and promise to pay back $150,052 at the end of 8 years.

_______ %

d. You borrow $18,000 and promise to make payments of $4,390.00 at the end of each year for 5 years.

_______ %

Effective rate of interest

Find the interest rates earned on each of the following. Round each answer to two decimal places.

a. You borrow $700 and promise to pay back $791 at the end of 1 year.

_______%

b. You lend $700 and the borrower promises to pay you $791 at the end of 1 year.

_______ %

c. You borrow $70,000 and promise to pay back $150,052 at the end of 8 years.

_______ %

d. You borrow $18,000 and promise to make payments of $4,390.00 at the end of each year for 5 years.

_______ %

Explanation / Answer

1.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

791=700*(1+r/100)^1

(1+r/100)=(791/700)

(1+r/100)=1.13

r=(1.13-1)*100

=13%

2.We use the formula:

A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

791=700*(1+r/100)^1

(1+r/100)=(791/700)

(1+r/100)=1.13

r=(1.13-1)*100

=13%

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.

150052=70000*(1+r/100)^8

(150052/70000)(1/8)=(1+r/100)

(1+r/100)=1.10

r=(1.10-1)*100

=10%

4.

Let interest rate be x%

At this rate;present value of annuity=18000

18000=4390/1.0x+4390/1.0x^2+4390/1.0x^3+4390/1.0x^4+4390/1.0x^5

Hence x=interest rate=7%

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