Question

Lamar borrowed S8000 at a rate of 13%, compounded quarterly. Assuming he makes no payments, how much will he owe after 10 years

Answer 1

Answer:

$28 753.61

Step-by-step explanation:

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

$A=P(1+i)^{n}$

"A" means final amount.

"P" means principal (starting amount).

"i" is interest, using $i=\frac{r}{c}$

"n" is number of compounding periods, using $n=t*c$

"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:

$A=P(1+\frac{r}{c})^{t*c}$

What we know:

P = 8000

r = 13%/100 = 0.13

c = 4

t = 10

Substitute into the formula:

$A=P(1+\frac{r}{c})^{t*c}$

$A=8000(1+\frac{0.13}{4})^{10*4}$

Simplify

$A=8000(1+0.0325)^{40}$

$A=8000(1.0325)^{40}$

Solve the exponent

$A=8000(3.59420143)$       Sometimes this step is not needed

$A=28753.6114$              Unrounded answer

Round to two decimal places (for cents).

$A=28753.61$                  Final Answer

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

Answer 2

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 = $P(1+\frac{R}{nX100} )^{nT}$

Now,

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

Amount = 8000($1+\frac{13}{4X100} )^{4X10}$

= 28753.61 (approx)