You’re planning a really big surprise trip for your 10-year anniversary. however, the internet is down and you know you need to buy the airline tickets during tomorrow’s flash sale. your 9 and 1/2-year investment of your wedding money, $18,000, earned 8.2% interest that compounded quarterly. how much money is in that account now?

The stated interest rate is still the nominal rate. To convert nominal to effective rate, the formula is:

r = (1 + i/n)^n - 1

where n=3 because there are 3 quarters in a year

r = (1 + 0.082/3)^3 - 1 = 0.084262

Then, we use the compounding interest formula. Since only half a year is needed to reach the 10-year anniversary, n = 0.5 years.

F = P(1+ r)^n

F = 18000(1 + 0.084262)^0.5

F = $18,743.02