Alonzo plans to retire as soon as he has accumulated $250,000 through quarterly payments of $5,000. If Alonzo invests this money at 5.4% interest, compounded quarterly, how long (to the nearest year) until can he retire?

Answer 1

quarterly payment = 5000
i = .054/4 = .0135
n = ?
Amount = 250000

5000(1.0135^n - 1)/.01535 = 250000
1.0135^n - 1 = .0135(50000) = .675
1.0135^n = 1.675
take log of both sides and use log rules
n log 1.0135 = log 1.675
n = 38.47 quarter years or appr 9 years and 7 months