mekhipalmer16
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Lamar borrowed S8000 at a rate of 13%, compounded quarterly. Assuming he makes no payments, how much will he owe after 10 years
Do not round any intermediate computations, and round your answer to the nearest cent.

Respuesta :

lavanyaande

The amount he needs to pay is $ 28753.61.

Step-by-step explanation:

Given,

Principal (P) = $ 8000

Time (T) = 10 years

Rate of interest (R) = 13%

The payment will be quarterly so, n = 4

To find the amount of compound interest.

Formula

Amount = [tex]P(1+\frac{R}{nX100} )^{nT}[/tex]

Now,

Putting the values of P, T, n and R we get,

Amount = 8000([tex]1+\frac{13}{4X100} )^{4X10}[/tex]

= 28753.61 (approx)

joy123333

Answer:

$28 753.61

Step-by-step explanation:

We will use the formula for total amount after compound interest.

[tex]A=P(1+i)^{n}[/tex]

"A" means final amount.

"P" means principal (starting amount).

"i" is interest, using [tex]i=\frac{r}{c}[/tex]

"n" is number of compounding periods, using [tex]n=t*c[/tex]

"r" is the annual interest rate as a decimal.

"t" is the time in years.

"c" is the compounding periods in a year. (annual = 1, quarterly = 4, etc...)

You can rewrite as a combined formula:

[tex]A=P(1+\frac{r}{c})^{t*c}[/tex]

What we know:

P = 8000

r = 13%/100 = 0.13

c = 4

t = 10

Substitute into the formula:

[tex]A=P(1+\frac{r}{c})^{t*c}[/tex]

[tex]A=8000(1+\frac{0.13}{4})^{10*4}[/tex]

Simplify

[tex]A=8000(1+0.0325)^{40}[/tex]

[tex]A=8000(1.0325)^{40}[/tex]

Solve the exponent

[tex]A=8000(3.59420143)[/tex]       Sometimes this step is not needed

[tex]A=28753.6114[/tex]              Unrounded answer

Round to two decimal places (for cents).

[tex]A=28753.61[/tex]                  Final Answer

Therefore, Lamar will owe $28 753.61 after 10 years.

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