Question

An investment is advertised as returning 3.1% every 3 months (quarterly), compounded quarterly. If $30,000 is invested, the growth can be modeled by the equation A(t) = 30,000(1.031)^4t. What is the equivalent annual growth rate for this investment (rounded to the nearest hundredth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 15 years?

Hint: Find the value of 1.031^4 on your calculator.

12.99% and $187,000
12.47% and $173,000
7.82% and $187,000
9.37% and $43,000

Answer 1

(1.031^4(15) = ( 1+r)^15
60 log 1.031 = 15 log (1 + r)
4log (1.031) = log ( 1 + r)

10^[4log(1.031)] = r + 1

10^[4log (1.031) ] - 1 =
r = 0.1299
= about 12.99%

So the answer would be 12.99% and $187,000.