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?

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Business

Imani Bass

Today, 06:05

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?

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Nikhil Terry · Answer 1

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