Capital value find the capital value of an asset that generates $7200 yearly income if the interest rate is as follows.
a. 5% compounded continuously
b. 10% compounded continuously

a. An asset that generates $7200 yearly income if the interest rate 5% compounded continuously, then its capital value is $140433.002

b. An asset that generates $7200 yearly income if the interest rate 10% compounded continuously, then its capital value is $68460.59

Step-by-step explanation:

For continuously compound interest

                     ---------------> eq.1

Where

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

t = number of years

A = amount after time t.

Let’s solve the equation

Where,

P is unknown

                     A = P + 7200 (asset after 1 year) ---------------> eq. 2

Case A:

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

Case B:

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

the answer is c

hope this !