Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?

y = 360(1.3)x
y = 360(0.3)x
y = 360(0.03)x
y = 360(1.03)x

Question

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?

y = 360(1.3)x
y = 360(0.3)x
y = 360(0.03)x
y = 360(1.03)x

marinos · Answer

At the beginning of the investment the balance of the account is $360. At the end of the first year, the balance of the account is the initial capital of $360 plus the interest it accrued, which is 3% * $360, so a total of $360 + 3% * $360 = (1+3%)*$360 = 1.03*$360 . At the end of the next year, the balance will be the latter amount plus its accrued interest, i.e. 1.03*$360 + 3%*1.03*$360 = (1+3%)*1.03*$360 = 1.03*1.03*$360 = 1.03^2 * $360
It is easy to see the pattern here. Can you say what will be the balance after x years, and hence conclude the answer to the problem?