Question

1. Your grandparents are trying to reduce the taxable amount of their estate, so they give you $18,000 this year – your inheritance early. You decide to save it for a down payment on a house. You invest it in the stock market and average a 9% return. How much will your money be worth when you cash it out for your down payment in 10 years, assuming it is compounded monthly?

Answer 1

Time Value of money means that the sum of money received today has more value than the same amount to be received in future.

There are 2 techniques to incorporate Time value of money in financial decision making:

a) Discounting - This technique is used to calculate the Present value of money to be received in future

b) Compounding - This technique is used to calculate the Future value of the present amount of money.

In this question,we have to find the future value of the amount $18,000. The formula of FV in case of Annual Compounding-

FV = PV * (1 + r) ^n

where FV= Future value

PV= Present Value

r = rate of interest

n = number of years for which compounding is to be done

But in case of non-annual compounding like monthly, quarterly, weekly, the Formula of FV is-

FV = PV * (1 + r/m)^^{n * m}

where m= number of times of compounding per year

Here, the PV = $18,000

r= 9% or 0.09

n= 10 years

m = 12 ( monthly compounding )

FV = 18,000 * (1 + 0.09/12) ^^{10* 12}

FV = 18,000 * (1.0075)^¹²⁰

FV = 18,000 * 2.45

FV = $44,124