Question

A)What is the present value of a security that will pay $45,000 in 20 years if securities of equal risk pay 6% annually? Do not round intermediate calculations. Round your answer to the nearest cent.

B)if you deposit $7,000 in a bank account that pays 5% interest annually, how much will be in your account after 5 years? Do not round intermediate calculations. Round your answer to the nearest cent.

C)Your parents will retire in 24 years. They currently have $280,000 saved, and they think they will need $1,950,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

Answer 1

a.Present value=45000*Present value of discounting factor(rate%,time period)

=45000/1.06^20

=45000*0.311804727

=$14031.21(Approx).

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.

A=7000*(1.05)^5

=$8933.97(Approx).

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.

1,950,000=280,000*(1+r/100)^24

(1,950,000/280,000)^(1/24)=(1+r/100)

(1+r/100)=1.0842

r=1.0842-1

=8.42%(Approx).