Respuesta :
Answer: the value of the account after 10 years is $2606
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 1800
r = 3.7% = 3.7/100 = 0.037
t = 10 years
Therefore,
A = 1800 x 2.7183^(0.037 x 10)
A = 1800 x 2.7183^(0.37)
A = $2606 to the nearest dollar
To solve such problems we must know about Continuous Compound Interest.
Continuous Compound Interest
[tex]A = Pe^{rt}[/tex]
where,
A is the principal amount after t number of years,
r is the rate at which the principal is been compounded, and P is the principal amount.
The value of Steve's account after 10 years will be $2,606.
Given to us
- Steve invests 1,800 in an account that earns 3.7% annual interest, compounded continuously.
- Time period money invested for 10 years,
Solution
As it is given in the problem, the account of Steve is compounding continuously.
Statement 1
Steve invests 1,800 in an account that earns 3.7% annual interest, compounded continuously.
- Principal amount = $1,800
- Rate of interest = 3.7% = 0.037
Statement 2
Time period money invested for 10 years,
- time period, t = 10 years
Value of the account
Substituting the values in the formula of Continuous Compound Interest,
[tex]A = Pe^{rt}[/tex]
[tex]\begin{aligned}A&=\$1800\times e^{0.037\times10}\\ &=\$2605.9\approx\$2606\\ \end{aligned}[/tex]
Hence, the value of Steve's account after 10 years will be $2,606.
Learn more about Compound Interest:
https://brainly.com/question/25857212
