Allyson Gomez invests $8,000 today in an investment that earns 6 percent per year (compounded annually) for 25 years. The average inflation rate is expected to be 1.8 percent per year. She will have much more than $8,000 in 25 years BUT what would this future amount be if expressed in today's dollars? a. $34,335 b. $21,981 c. $52,306 d. $12,496 e. $21,839

B

Explanation:

The first thing to do here is to calculate what the amount of money invested would be in 25 years given the interest rate.

Mathematically, that can be written as;

V = P (1 + r) ^n

Where V is the future value

P is the present value which is $8,000

r is interest rate which is 6% (6/100 = 0.06)

n is the number of years which is 25 years

Now plugging these values into the equation, we have

V = 8,000 (1 + 0.06) ^25

V = 8,000 (1.06) ^25

V = $34,334.97 which is approximately $34,335

We can now proceed to get what this future value would be today if we take the inflation rate into consideration

Mathematically, this can work as follows

P = V (1 + i) ^n

Where P is the present value of the money when the inflation is taken into consideration

V is the future value of the money which was calculated from above as $34,335

i is the inflation rate which is 1.8% per annum = (1.8/100 = 0.018)

n is the number of years which is 25

Substituting these values, we have;

P = 34,335 / (1 + 0.018) ^25

P = 34,335 / (1.018) ^25

P = 21,980.75

Which is approximately P = $21,981