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The savings plan balance after 24 months with an apr of 2.5% and monthly payments of $400 is $9,833.55 .
What is ordinary annuity?
An ordinary annuity is a series of regular payments made at the end of each period, such as monthly or quarterly. In an annuity due, by contrast, payments are made at the beginning of each period. Consistent quarterly stock dividends are one example of an ordinary annuity; monthly rent is an example of an annuity due.
Calculating the Future Value of an Annuity Due
An annuity due, you may recall, differs from an ordinary annuity in that the annuity due's payments are made at the beginning, rather than the end, of each period.
The formula for the future value of an annuity due is as follows:
[tex]FV_{Annuity Due} = C * [\frac{(1+i)^{n}-1 }{i} ] * (1+i)[/tex]
where:
C = cash flow per period
i = interest rate
n = number of payments
According to the question
The savings plan balance after 24 months
i.e
Number of payments = 24
Interest rate (i) = 2.5%
= 0.025
Interest rate (i) for month = 0.025/12
= 0.00208
Cash flow per period = $400
Now, By using the Future Value of an Annuity Due
we will get the value of savings plan balance
[tex]FV_{Annuity Due} = C * [\frac{(1+i)^{n}-1 }{i} ] * (1+i)[/tex]
Now ,
substituting the values in the formula
[tex]= 400 * [\frac{(1+0.00208)^{24}-1 }{0.00208} ] * (1+0.00208)[/tex]
[tex]= 400 * [\frac{(1.00208)^{24}-1 }{0.00208} ] * (1.00208)[/tex]
= $9,833.55
Hence, the savings plan balance after 24 months with an apr of 2.5% and monthly payments of $400 is $9,833.55 .
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