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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?

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 ...

$2.19