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You would like to have ​$4000 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4.5​% compounded semiannually. a. Use one of the formulas below to determine how much you should deposit at the end of every six months.

Respuesta :

Answer:

666.70 at the end of every six months.

Step-by-step explanation:

At the end of  every six months deposit amount is 666.70

What is compound interest ?

Compound interest is the interest paid on both principal and interest, compounded at regular intervals.

Formula of compound interest :

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

where,

A = final amount

P = initial principal

n = time in years

r = rate per annum

According to the question

Final Amount needed for a special vacation (A) = ​$4000

Time in years needed to collect Amount (n) =  3 years

Rate per compounded semiannually (r) = 4.5​%

Substituting values in formula for six months

Now time (n) = 3 * 6 = 18 years

using formula of compound interest

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]

[tex]4000 = P(1.045 )^{18}[/tex]

now,

P = 666.70

Hence, at the end of  every six months deposit amount is 666.70

To know more about compound interest here:

https://brainly.com/question/14295570

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