James and Terry open a savings account that has a 2.75% annual interest rate,compounded monthly.They deposit $500 into the account each month.How much will be in the account after 20 years?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the amount in the account after t years
P = the initial deposit or principal (in this case, $0)
r = the annual interest rate (2.75%)
n = the number of times the interest is compounded per year (12, for monthly)
t = the number of years (20)

We also know that James and Terry deposit $500 into the account each month, which means that the effective monthly deposit is $1,000 (since there are two of them).

Plugging in the values, we get:

A = 0(1 + 0.0275/12)^(12*20) + (1000*12)*( (1 + 0.0275/12)^(12*20) - 1)/(0.0275/12)
A = $159,744.59

Therefore, the best choice is B.

James and Terry Open a Savings Account That Has a 2.75