Answer:
$18,453.40
Explanation:
the easiest way to determine how much money Matt is going to save is by using the future value annuity factor. Using a future value annuity table, we must look for the value that correspond to 5% interest and 10 periods = 13.181
Now we multiply our annuity factor times the amount of money that Matt saves every 6 months = $1,400 x 13.181 = $18,453.40
When Matt graduates from college he should have saved $18,453.40.
Matt will save $17609.2 at the end of the fifth year, if his savings earn 10% annually (or 5% every six months).
The future value of an annuity is the group of repeated payments for a specific future date, deducted a certain refund rate, or a discount rate. The higher the discount rate, the greater the annuity amount.
Formula of future value of an annuity:
[tex]FV = P \times[ \dfrac{(1+r)^{n}-1 }{r}]\\[/tex]
As per the information:
Payment is $1,400
Rate is 10%, semiannually compounded that will become 5%
Number of periods is 5 years, compounded semiannually will be equal to 10 ( 5 multiplied by 2)
Future value of annuity is equal to :
[tex]\rm\,FV = P \times[ \dfrac{(1+0.05)^{10} - 1}{0.05}]\\\\\rm\,FV = 1,400 \times[ \dfrac{(1+0.05)^{10} - 1}{0.05}]\\\\FV = 1,400 \times 12.578\\\\\rm\,FV = \$17609.2[/tex]
Hence, matt will save $17609.2 at the end of the fifth year.
Learn more about Future value of annuity, refer:
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