Question

use the continuous compound interest formula to find the indicated value.

A= $76,000

P=$57,756

R=6.1%

T= ?

Don’t round until the final answer. Then round to two decimal places as needed.

Answer 1

Continuously compounded interest means that the principal is constantly earning interest and the interest keeps earning on the interest earned.

Formula is                                                                                                                                                         

A = P* e^ (rt)                                                                                                                                                    

Where                                                                                                                                                 

Amount = 76000

Payment = 57756                                                                                                                                                            

Interest rate = 0.061                                                                                                                                      

Term =?                                                                                                                                              

e = a mathematical constant having value of 2.7183

Let’s put all the values in the formula

76000 = 57756 * 2.7183^ (0.061* t)

76000/ 57756 = 2.7183^ (0.061* t)

1.3159 = 2.7183^ (0.061* t)

Take log on both sides

Log (1.3159) = log 2.7183^ (0.061* t)

Log (1.3159) = (0.061* t) * log 2.7183

0.11922 = (0.061* t) * 0.4343

(0.061* t) = 0.11922/ 0.4343

(0.061* t) = 0.2745

t = 0.2745/ 0.061

t = 4.5 years

so the time is 4.5 years