# Present value and future value - personal finance

1.A)The formula to calculate the value of $1 put into savings today is fv = pv*((1+i)^n). The variables are:

fv = future value

pv = present value

i = interest rate per period

n = the number of periods - an exponent in the formula

a. What does the exponent in this case state that you need to do mathematically to the (1 + i) segment of the formula?

b. Select an interest rate and number of periods. Calculate the future value of $1000. How much money would you have at the end of the period you determined if you invested $1000 today (pv)?

B). Often in personal finance we want to know what our $1 investment today will be worth in 20 years. In business however, there is more concern with answering the question: "If I receive $100 in 5 years, what is that worth today?" To answer this question, modify the formula fv = pv*((1+i)^n) and use the reciprocal. Simply stated, the reciprocal of a number is 1 divided by the number; the reciprocal of 10, for example, is 1/10. In the formula above, we divide both sides by ((1+i)^n), which creates a new formula where the fv is multiplied by the reciprocal of the original: fv*(1/((1+i)^n))=pv. Use the interest rate and number of periods in DQ #1.A Calculate the present value of $100 received in the future. What would the value of $100 in the future be today given the interest rate and number of periods you selected?

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#### Solution Preview

a. What does the exponent in this case state that you need to do mathematically to the (1 + i) segment of the formula?

The exponent tells you that you must multiply (1 + i) by ...