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Reuben has always dreamed of opening a café by the seaside. He decides he will save to help open the café by depositing money in an ordinary annuity that earns 5.4% interest, compounded monthly. Deposits will be made at the end of each month. How much money will he need to deposit into the annuity each month for the annuity to have a total value of $24,000 after 9 years? Do not round intermediate computations, and round your final answer

Respuesta :

Answer:$ 66.5

Step-by-step explanation:

Using ordinary Annuity formula

[tex]FV=\frac{P\times \left [ \left ( 1+r\right )^n-1\right ]}{r}[/tex]

FV=future value=$24000

P=monthly payment

r=rate of interest =5.4%

for monthly [tex]r=\frac{5.4}{12}=0.45%[/tex]

n=number of payments  [tex]=9\times 12=108[/tex]

[tex]24000=\frac{P\times \left [ \left ( 1+0.0045\right )^{108}-1\right ]}{0.0045}[/tex]

[tex]108=P\times (1.6240)[/tex]

P=$ 66.501

sop monthly deposit of  $ 66.5 is required.

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