Question

Answer the following problems

a. If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

b. What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?

c. Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

d. If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?

Answer 1

A) $FV=PV (1+r)^n$

Where

PV=$10000

r= 10% or 0.1

n= 5

$FV_5=\$10000(1+0.1)^5$

$FV_5=\$16105.1$

B) $PV=FV (1+r)^{-n}$

Where

FV=$5000

r= 7% or 0.07

n= 20

$PV=\$5000(1+0.07)^{-20}$

$PV=\$1292.10$

The present value of the security is $1292.10

C) Given that

$FV=PV (1+r)^n$

$r={\sqrt[n](\frac{FV}{PV}})-1$

Where

FV=$1000000

PV=$250000

n=18

$r=\sqrt[4]({\frac{\$1000000}{\$250000})}-1$

$r=0.08 \space{or}\space{8\%}$

D) if $FV=PV (1+r)^n$

And $FV=2PV$

$2PV=PV (1+r)^n$

$2=(1+r)^n$

Taking the log of both sides

$log2=nlog(1+r)$

$n=\frac{log2}{log(1+r)}$

Where

r=6.5% or 0.065

$n=\frac{log2}{log(1+0.065)}$

$n=11\space{years}$