Final answer:
To find the balance of an account after 5 years with a $2000 deposit and a 3.75% interest rate compounded monthly, you use the compound interest formula A = P(1 + r/n)^(nt). Plugging in the numbers provided gives A = $2000(1 + 0.0375/12)^(60). Using a calculator will give the exact future balance.
Step-by-step explanation:
You have asked how much money will be in an account after 5 years if $2000 is deposited into an account that pays 3.75% interest compounded monthly.
To calculate the future balance of an account with compound interest, we use the formula:
A = P(1 + r/n)^(nt), where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for, in years.
In your case, P = $2000, r = 0.0375 (3.75%), n = 12 (since the interest is compounded monthly), and t = 5 years.
Substituting the values in the formula gives you:
A = $2000(1 + 0.0375/12)^(12*5) = $2000(1+0.003125)^(60)
After simplifying, the future balance A can be calculated. You can use a calculator to determine the exact amount.