Brianna deposits $150 at the end of each quarter into an account that pays 8% compounded quarterly for 9 months. calculate the amount in the account at the end of the period.
I did this ..
150[(1 + .08)^9x3 – 1]
3
divide the top half by .08/3
= 150[(1+0.027)^27-1]
divide the top half by the bottom half 0.027
= 5,850.34
that can’t be right only after 9 months.
To calculate the amount in the account at the end of the period, you need to use the formula for the future value of an ordinary annuity, which is:
Future Value = Payment * [(1 + interest rate per period)^(number of periods) - 1] / (interest rate per period)
In this case, the payment is $150, the interest rate per period is 8% divided by 4 quarters (0.08/4 = 0.02), and the number of periods is 9 months multiplied by 3 quarters (9 * 3 = 27).
Now let's plug in these values into the formula:
Future Value = 150 * [(1 + 0.02)^27 - 1] / 0.02
Future Value = 150 * [(1.02)^27 - 1] / 0.02
To solve this equation, you need to calculate (1.02)^27:
(1.02)^27 = 1.747422051
Now, let's substitute this value back into the formula:
Future Value = 150 * (1.747422051 - 1) / 0.02
Future Value = 150 * 0.747422051 / 0.02
Future Value ≈ $5,610.67
So, the amount in the account at the end of the period is approximately $5,610.67, which seems to be the correct amount.