1200 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest year, how long will it take for the account value to reach 8200 dollars?

The time required is about 75 years 3 months

Step-by-step explanation:

We know that the simple interest is expressed as

A = P (1 + rt)

A = final amount = $8200

P = initial principal

: balance=$200

r = annual interest rate 7.75%

7.75/100 = 0.0775

t = time (in years)

Substituting our data into the expression we have

8200 = 1200 (1+0.0775*t)

8200=1200+93t

93t = 8200-1200

93t = 7000

t = 75.27

The time required to get a total amount, principal plus interest, of $8,200.00 from simple interest on a principal of $1,200.00 at an interest rate of 7.75% per year is 75.27 years (about 75 years 3 months)