Determine the amount of money in a saving account at the end of five years, given an initial deposit of $5,000 and a 12 percent annual interest rate when interest is compunded a) annually b) semiannually c) quarterly
To determine the amount of money in a savings account at the end of five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount (money in the account at the end of five years)
P = principal (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
a) When interest is compounded annually (n = 1):
A = 5000(1 + 0.12/1)^(1*5)
A = 5000(1.12)^5
A ≈ $8,235.05
b) When interest is compounded semiannually (n = 2):
A = 5000(1 + 0.12/2)^(2*5)
A = 5000(1.06)^10
A ≈ $8,427.07
c) When interest is compounded quarterly (n = 4):
A = 5000(1 + 0.12/4)^(4*5)
A = 5000(1.03)^20
A ≈ $8,598.97
So, at the end of five years, with an initial deposit of $5,000 and a 12 percent annual interest rate, the amount of money in the savings account will be approximately:
a) $8,235.05 when compounded annually
b) $8,427.07 when compounded semiannually
c) $8,598.97 when compounded quarterly.