Question

You have $1000 to invest in an account and need to have $1500 in one year. What interest rate would you need to have in order to have this if the amount is compounded quarterly? Round your answer to the nearest percent.

Answer 1

Let r be the interest rate. Then:
1000(1+r/4)^4=1500
(1+r/4)^4=1.5
ln (1+r/4)^4= ln 1.5
4 ln (1+r/4)=ln 1.5
ln (1+r/4)=0.10136627702704109549450327886609
1+r/4=e^0.10136627702704109549450327886609=1.1066819197003215924087902734403
r/4=0.1066819197003215924087902734403
r=0.42672767880128636963516109376133 or 42.67%, compounded quarterly. ☺☺☺☺