How much would 1,000,000 due in 10 years be worth today if the discount rate was 5%. If the discount rate was 10%. discuss how and why the results are different at the different rate
An amount will be worth $1 000 000 in the future (in this case 10 years). To determine how much to invest NOW to ensure that the investor will get his return in 10 years, we use the future / present value formula to find the "discounted value" (ie the present value).
The formula is: Fv=P(1+r/100)^t
and to calculate the present value of money:
P = Fv/(1+(r/100))^t or P=Fv(1+r/100)^-t
where Fv= future value= 1 000 000, P=present value, r or i=interest rate = 5% = 5/100 = 0.05 and t= time (in years)= 10. Therefore :
P= 1 000 000/(1+0.05)^10
Therefore = $613 913,25 (@ 5%).
For 10%, r=10/100= 0.1. Therefore P=1 000 000/(1+0.1)^10
Therefore = $385 543,29 (@ 10%).
The results differ at the different rates. The higher the "discounted" rate, the lower the required investment. This reveals that money has a time value and, to secure a specific amount in a certain number of years, it is wise to calculate its present value in order to be certain that a suitable amount is invested. Then, if all factors remain constant and the discount rate is 5% or 10% , the amounts are:
$613 913,25 (@ 5%) and $385 543,29 (@ 10%)