Question

Use the compound interest formula to find the present value​ P, for the following given values. A=$12,700 i=0.046 n=86 P=$ ​(Round to the nearest​ cent.)

Answer 1

Hey there
The formula of the compound interest is
A=p (1+i)^n
A future value 12700
P present value?
I interest rate 0.046
N time 86
Solve the formula for p
P=A ÷ (1+i)^n
P=12,700÷(1+0.046)^(86)
P=265.51

Answer 2

Hey there!

The compound interest formula will be the following:

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

Since you haven't been given the amount of years, you can just omit this. You've already been given all of the information you need, so just plug everything into this equation and solve for P:

A = $12,700
i = 0.046
n = 86

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

$12700 = P(1+ \frac{0.046}{86})^{86}$

Make sure that you follow PEMDAS!

$12700 = P(1.00053488)^{86}$

$12700 = P(1.047061199296832)$

$\frac{12700}{1.047061199296832} = \frac{P(1.047061199296832)}{1.047061199296832}$

$12129.185962127959125 = P$

$12,129.19 = P$

You can check this by plugging this number in for P and solving for A to see if it equals the A you were given. 

$A = 12129.19(1+ \frac{0.046}{86})^{86}$

$A = 12129.19(1.047061199296832)$

$A = 12129.19(1.047061199296832)$

$A = 12,700$

Your answer will be P = 12,129.19. 

Hope this helped you out! :-)