A couple needs $15,000 as a down payment for a home. If they invest the $10,000 they have at 8% compounded quarterly, how long will it take for the money to grow into $15,000?

Answer 1

10000(1.02)^n = 15000 , where n is the number of quarter years.
1.02^n = 1.5
take log of both sides
log 1.02^n = log 1.5
n log 1.02 = log 1.5
n = log 1.5/log 1.02 = 20.475 quarters
= 5.12 years , 20.475 quarters or 61.4 months
take your pick