The formula is A = (R((1+ i)^n -1))/i
R is the regular payments
i is the interest
n is the number of compounding periods
Determine the amount of each ordinary simple annuity.
A) $650 deposited every 6 months for 8 years at 9% per year compounded semi-annually.
B) $375 deposited every month for 6 years at 5.9% per year compounded monthly
CAN SOMEONE HELP ME GET STARTED ON THESE QUESTIONS? I started it but I was getting different answers from the textbook.
Um, I guess plug in the numbers into the formula? I mean, I don't really get your problem.
I’m getting different answers
To determine the amount of each ordinary simple annuity, we can use the formula:
A = (R((1+ i)^n -1))/i
Let's start by calculating the amount for question A:
A) $650 deposited every 6 months for 8 years at 9% per year compounded semi-annually.
In this case:
R = $650 (the regular payment)
i = 9%/2 (since it is compounded semi-annually, we divide the annual interest rate by 2)
n = 8 years * 2 (since it is compounded semi-annually, we multiply the number of years by 2 as there are two compounding periods per year)
Now, let's plug in the values into the formula and solve for A:
A = (650 * ((1 + (9%/2))^(8*2) - 1)) / (9%/2)
Simplifying the equation further:
A = (650 * ((1 + 0.045)^(16) - 1)) / (0.045)
Using a calculator or spreadsheet, we can find the value of A to be approximately $7,556.09.
Now, let's move on to question B:
B) $375 deposited every month for 6 years at 5.9% per year compounded monthly.
In this case:
R = $375 (the regular payment)
i = 5.9%/12 (since it is compounded monthly, we divide the annual interest rate by 12)
n = 6 years * 12 (since it is compounded monthly, we multiply the number of years by 12 as there are twelve compounding periods per year)
Now, let's plug in the values into the formula and solve for A:
A = (375 * ((1 + (5.9%/12))^ (6*12) - 1)) / (5.9%/12)
Simplifying the equation further:
A = (375 * ((1 + 0.00492)^(72) - 1)) / (0.00492)
Using a calculator or spreadsheet, we can find the value of A to be approximately $28,872.11.
Make sure to double-check the calculations and ensure that the values you used for R, i, and n are accurate, as discrepancies may lead to different answers from the textbook.