A family deposited $500 in a money market account to save for a trip. If their money earns 1.5% interest compounded quarterly, how much will they have in one year?

Question

Eva Adamson · Accepted Answer

#color(indigo)("In 1 year they will have " $530.68# #P = $500, N = 1 Year = 4 " Quarters", R = 1.5% " Quarterly"# #"Formula for compound interest " A = P * (1 + R/100)^N# #A = 500 * (1 + 0.015)^4 = $530.68#

Nathan Axel · Answer

undefined To calculate the amount in one year, use the formula A = P(1 + r/n)^(nt), where:
A is the amount after the time period,
P is the principal amount ($500 in this case),
r is the annual interest rate (1.5% expressed as a decimal, so 0.015),
n is the number of times the interest is compounded per year (quarterly, so 4),
and t is the time the money is invested for (1 year).

Plugging in the values:
A = 500(1 + 0.015/4)^(4*1)

Calculate the expression inside the parentheses first:
1 + 0.015/4 = 1.00375

Then raise it to the power of (4*1):
(1.00375)^(4) ≈ 1.015063

Finally, multiply by the principal amount:
A ≈ 500 * 1.015063 ≈ $507.53

So, after one year, they will have approximately $507.53 in the money market account.