Early last year, the Zoe Growth Fund ran advertisements in the financial pages of major newspapers. The "ad" had primarily empty space containing the simple message:
$20,000 INVESTED IN ZOEINVESTMENT GROWTH FUND IN 1962
WOULD BE WORTH $9.40 MILLION TODAY
What compound annual rate of return did the fund realize over the period ending December 31 last year? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example 34.56%
The correct answer was: 13.99%
The usual maturity value is computed by FV=PV(1+i)n, where:
PV is the principal value,
i=j/m is the periodic interest rate,
and n is the number of compoundings in a year × the number of years in the term.
In this case, m=1, so i=j. Solving for i in the above formula gives i = (FV/PV)1/n-1 = 13.99%.
You will receive 0 marks out of 5 for this question.
i need help knowing how to get the answer. i tried and it keeps coming different answer..very confused!!
5 answers
after interest rate r is applied for n years compounded yearly. r is as a decimal fraction, like 15% is .15
final value = 20,000 (1+r)^(2009-1962)
9400000 = 20,000(1+r)^47
470 = (1+r)^47
log 470 = 47 log(1+r)
2.672=47 log(1+r)
log(1+r) = .05685
(1+r) = 10^.05685
1+r = 1.13986
r = .13986
so 13.99 % is what I get
4 answers