Suppose you deposit$2,000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn, determine how much will be in the account after 3 years.
A. $1,847.12
B. $2,249.73
C. $7,432.62
D. $7,876.25
The amount in the account after 3 years can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Here, P = $2,000, r = 4% = 0.04, n = 1 (interest compounded annually), t = 3 years.
A = 2000(1 + 0.04/1)^(1*3)
= 2000(1 + 0.04)^3
= 2000(1.04)^3
= 2000(1.124864)
= $2,249.73
Therefore, the option that represents the amount in the account after 3 years is B. $2,249.73.