Question

Thirty years ago, your rich uncle invested $10,000 in an aggressive (i.e. risky) mutual fund. Much to your uncle's chagrin, the value of his investment declined by 18% during the first year and then declined another 31% during the second year. But your uncle decided to stick with this mutual fund, reasoning that long-term sustainable growth of the U.S. economy was bound to occur and enhance the value of his mutual fund. Twenty-eight more years have passed, and your uncle's cumulative return over the 30-year period is a whopping 707%! If the value of the original investment now is $80,700: What is the spending power equivalent in terms of real dollars 30 years ago if inflation has averaged 6% per year over the past 30 years? Round to nearest integer What is the real compound interest rate earned over the 30-year period? Round to two decimal places

Answer 1

Question 1

$1 30 years ago would equal $5.74 now at 6% inflation.

X =FV(B1,B2,0,-1) ВЗ А В 0.06 Inflation 1 2 Time in years 30 3 Value of $1 now =FV(B1,B2,0,-1)

fx X =FV(B1,B2,0,-1) А В 1 Inflation 6% 2 Time in years 30 Value of $1 now $ 3 5.74 83

Question 2

The nominal return can be calculated as we know the initial amount invested, final value of the investment and the period. The rate function can be used for this.

The real rate is calculated using Fischer's equation.

(1+nominal rate) = (1+real rate)*(1+inflation)

Thus

real rate = [(1+nominal rate)/(1+ real rate)] - 1

E(1+B5)/(1+B1))-1 В6 A В Inflation 0.06 1 2 Time in years 30 3 Amount invested 10000 4 Value of investment 80700 |ERATE(B2,0,-BЗ,В4) (1+B5) /(1+B1))-1 5 Nominal Rate of Return Real Rate of Return 6

fix X ((1+B5)/(1+B1)) В6 В 1 Inflation 6% 2 Time in years 30 $10,000.00 $80,700.00 3 Amount invested 4 Value of investment 5 Nominal Rate of Return 7.21% 6 Real Rate of Return 1.14%