SOLUTION: Sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000?

Question 1164315: Sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P=Po(1+(r/t))^n
400000=250000(1+.03)^nt, the nt being the total number of times it is compounded.
1.6=1.03^nt
ln both sides
0.4700=nt ln 1.03
nt=15.901
t=3.975 years. After 15 quarters it will not be 400000 but after 16 it will be more than 400000.
Rough check
12% of 250000 is 30000
four years of that without compounding would be 120000 more or 370000
with compounding, the above answer is reasonable.
RELATED QUESTIONS
A sum of $2500, 000 earns interest at a rate of 12% per year compounded quarterly. How... (answered by ikleyn,solver91311)

A sum of $2500, 00 earns interest at a rate of 12% per year compounded quarterly. How... (answered by greenestamps,josgarithmetic,ikleyn)

A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long (answered by solver91311,ikleyn)

A local university is planning to invest $500,000 every 3 months in an investment which... (answered by Theo)

a local university is planning to invest $ 500,000 every 3 months in an investment which... (answered by ikleyn)

A local university is planning to invest $500,000 every 3 months in an investment which... (answered by CPhill)

how long will it take for an investment to double if it earns 6.25% interest per year... (answered by mananth)

How long will it take an investment of $1,000 to double if the investment earns interest... (answered by mananth)

How long will it take an investment of $2000 to double if the investment earns interest... (answered by mananth)