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Funds are deposited in a savings account at an interest rate of 8% per annum. If the interest is compounded semi-annually, what is most nearly the initial amount that must be deposited to yield a total of $10,000 in 1?

Respuesta :

Answer:

Initial amount will be $9238.454

Explanation:

We have given amount after 1 year A = $10000

Rate of interest r = 8%

Time t = 1 year

Interest is compounded quarterly

So time period = 4

And rate of interest [tex]=\frac{8}{4}=2[/tex] %

We have to find the initial amount P

Final amount is given by [tex]A=P(1+\frac{r}{100})^n[/tex]

[tex]10000=P(1+\frac{2}{100})^4[/tex]

[tex]10000=P\times 1.02^4[/tex]

[tex]10000=P\times 1.0824[/tex]

P = $9238.454