determine the amount of each ordinary simple annuity. deposits of $2550 for 7 years at 9.7% per year compounded annually
Search instead for determine the amount of each ordinary simple annuity. deposits of $2550 for 7 years at 9.7% per year compounded annually.
B) Deposits of 1380 for 4 years at 10% per year compounded semi annually.
To determine the amount of each ordinary simple annuity, you can use the formula:
A = P * [(1 + r)^n - 1] / r
where:
A = Amount of each annuity payment
P = Deposit amount
r = Interest rate per compounding period
n = Number of compounding periods
Let's calculate the amount of each annuity payment for the given scenario:
B) Deposits of $1380 for 4 years at 10% per year compounded semiannually.
First, we need to convert the annual interest rate to a semiannual interest rate:
Semiannual interest rate = Annual interest rate / 2 = 10% / 2 = 5%
Next, we calculate the number of compounding periods:
n = Number of years * Number of compounding periods per year
n = 4 * 2 = 8 semiannual periods
Now, we can substitute the values into the formula:
A = 1380 * [(1 + 0.05)^8 - 1] / 0.05
Calculating this expression will give us the amount of each annuity payment for the given scenario.
Please note that I have assumed that the annuity payments are made at the end of each period (ordinary annuity). If this is not the case, please let me know so I can adjust the calculation accordingly.
To determine the amount of each ordinary simple annuity, you would need to use the formula for the future value of an ordinary simple annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity
P = Payment or deposit amount
r = Interest rate per period
n = Number of periods
Now let's calculate the amount of each ordinary simple annuity for both scenarios.
A) Deposits of $2550 for 7 years at 9.7% per year compounded annually:
Using the formula, we have:
P = $2550
r = 0.097 (9.7% expressed as a decimal)
n = 7
FV = $2550 * ((1 + 0.097)^7 - 1) / 0.097
Calculating this expression will give us the future value of the annuity, which represents the total amount at the end of the 7-year period.
B) Deposits of $1380 for 4 years at 10% per year compounded semi-annually:
First, we need to find the interest rate per period by dividing the annual interest rate by the number of periods in a year. Since the interest is compounded semi-annually, there are 2 periods in a year.
r = 0.1 / 2 = 0.05 (10% per year divided by 2 for semi-annual compounding)
Now we can use the formula with the updated values:
P = $1380
r = 0.05
n = 4
FV = $1380 * ((1 + 0.05)^4 - 1) / 0.05
Calculating this expression will give us the future value of the annuity, representing the total amount at the end of the 4-year period.
Since these are simple, ordinary annuities, the regular deposits happen at the same frequency as interest is applied, and we can use this formula:
FV = R [(1 + i)^n] / i
A)
FV = 2550 [(1 + 0.097)^7] / 0.097
FV = 2550 [1.097^7] / 0.097
FV = $ ______. __ (Round to 2 decimal places)
B) This question doesn't clearly state whether the $1380 regular deposits are semi-annually, to match when the interest is applied. If they are, you can use the above formula, remembering to adjust i and n accordingly (If not, it may be that you are expected to use a regular semi-annual deposit of $1380/2 = $690).