Question

Practice Time Value of Money Problems

 1. How much will be in an account at the end of 5 years if you deposit $10,000 today at 8.7% annual interest, compounded semi-annually?

 2. What is the balance at the end of 10 years if $2.500 is deposited today and the account earns 4% interest annually? What about if it's quarterly interest? Which one should be more and why?

 3. Suppose you want to have $500,000 saved by the time you reach 30 years old. You are 20 years old today. If you can earn 5.73% annually on your savings, how much do you need to invest today? Do you need to invest more or less if the interest rate increases to 7.9%?

Answer 1

(1)

FV=PV(1+r/2)2n, when the interest is compounded semi-annually

Here FV means Future Value, PV means Present vallue, r is required rate of return, n is term.

Substituing given values in the above,

FV= $10000(1+8.7%/2)2*5

FV=$10000((1+4.35%)10

FV=$15308( rounded off)

So, the value at the end of 5 years would be $15308

(2)

[a]

FV=PV(1+r)n, when the interest is compounded annually

Here FV means Future Value, PV means Present vallue, r is required rate of return, n is term.

Substituing given values in the above,

FV= $2500(1+4%)10

FV=$3701( rounded off)

So, the value at the end of 10 years would be $3701

[b]

FV=PV(1+r/4)4n, when the interest is compounded quarterly

Here FV means Future Value, PV means Present vallue, r is required rate of return, n is term.

Substituing given values in the above,

FV= $2500(1+4%/4)4*10

FV=$2500((1+1%)40

FV=$3722( rounded off)

So, the value at the end of 5 years would be $3722

The investment generates $21 higher when the interest compounds quarterly, relative to when it compounds annually.

This is because Compound interest adds the interest earned based on the terms of investment as a part of principle of the investment whenever it computes the interest.Which is the very reason why the investment compounded quarterly gives higher return in relation to when compunded annually, due to the frequency of the compounding of interest.

(3)

[a]

FV=PV(1+r)n, when the interest is compounded annually

Here FV means Future Value, PV means Present vallue, r is required rate of return, n is term.

Substituing given values in the above,

$500000= PV(1+5.73%)10

PV=$286410( rounded off)

So, the value at year 0 would be $286410

[b]

FV=PV(1+r)n, when the interest is compounded annually

Here FV means Future Value, PV means Present vallue, r is required rate of return, n is term.

Substituing given values in the above,

$500000= PV(1+7.9%)10

PV=$233752( rounded off)

So, the value at year 0 would be $233752

Unlike compounding, Present value is found through discounting. In compounding higher the rate of return higher the Future value,while in discounting higher the rate of return lower will be its present value.

In the given case the 2o year old has to invest only $233752 today to earn $500000 at 30years of age if the interest rate is 7.9% and he has to pay $286410 today to earn $500000 at 30 years of age if the interest rate is 5.73%