Question

Find the interest rate for a $7500 deposit accumulating to $12,042, compounded annually for 8 years. The interest rate is %. (Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

1)Given data:

Principal Amount (P) = $7500

Accumulated amount(A) = $12,042

compounded annually , so n=1

Time (t) = 8 years

Need to find intrest rate.

We know that compound intrest formula:

$A=P(1+\frac{r}{n})^{nt}$

Where, A = Final amount

            P = Principal Value

            r = Intrest rate

           n = no.of times intrest accumulated in the time

           t = Time in years

12042 = 7500(1+1+2

12042 = 7500(1 + r)

12042 7500 = (1 + r)

1.6056 =(1+ r)

$1.6056^{ \frac{1}{8}}=(1+r)$

$1.06=(1+r)$

$r=1.06-1=0.6$

Therefore r is 60%.

2)Given data:

Time (n)= 17 years

Intrest rate(r)= 5.4% = 0.054

Price =$ 6000

We know the formula for Zero coupon bond is

$Price of bond = \frac{Face Value}{(1+r)^{n}}$

Need to find Face Value:

Therefore Face Value = $ 14670.4

3)Given data:

Time(n) = 20 years

Intrest rate(r)= 6.02% = 0.0602

Price =$ 8500

We know the formula for Zero coupon bond is

$Price of bond = \frac{Face Value}{(1+r)^{n}}$

Need to find Face Value:

Therefore Face Value = $ 27363.7

4)Given data:

Intrest rate(r)= 4%=0.04

No.of compounding periods (N)=2

We know the formula for APY is

$APY=(1+ \frac{r}{N})^{N}-1$

$APY=(1+ \frac{0.04}{2})^{2}-1$

Therefore APY = 0.0404 = 4.04%

5)Given data:

Intrest rate(r)= 6%=0.06

No.of compounding periods (N)=4 (compounded Quarterly)

We know the formula for APY is

$APY=(1+ \frac{r}{N})^{N}-1$

$APY==(1.015)^{4}-1=0.06136$

Therefore APY = 0.06136 = 6.13%

Finally this is the answer and if you have any doubts please let me know in the comment section.Thank you.