Question
Matt invests 4,612 in a retirement account with a fixed annual interest rate of 4% compounded continuously How long will it take for the account balance to reach 8,403.61 12 years 13 years 15 years 14 years
Solution
4.2
(131 Votos)
Alejandro
Mestre · Tutor por 5 anos
Resposta
To solve this problem, we will use the formula for continuous compounding interest, which is given by:
where:-
is the amount of money accumulated after time
,-
is the principal amount (the initial amount of money),-
is the annual interest rate (in decimal form),-
is the time the money is invested for,-
is the base of the natural logarithm.Given:-
-
We need to find
.First, we rearrange the formula to solve for
:
Now, we plug in the given values:
Calculate the fraction inside the logarithm:
Now, take the natural logarithm of this value:
Finally, divide by the interest rate:
Since we are looking for the time in years and the options are whole numbers, we round to the nearest whole number:
Therefore, it will take approximately 15 years for the account balance to reach \$8,403.61.The correct answer is:15 years