You invest $100,000 in an account with an annual interest rate of 4.5%, compounded semiannually. How much money is in the account after 10 years? Round your answer to the nearest whole number.
Pt = Po(1+r)^n.
r = (6/12) * 4.5% = 2.25% = 0.0225 =
Semi-annual % rate expressed as a decimal.
n = 2 comp./yr * 10 yrs. = 20 Compounding periods.
Pt = 100,000(1.0225)^20 = $156,050.92.
To calculate the amount of money in the account after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money after time t
P is the principal amount (initial investment)
r is the annual interest rate (expressed in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount (initial investment) is $100,000, the annual interest rate is 4.5% (or 0.045 as a decimal), the interest is compounded semiannually (n = 2), and the time is 10 years (t = 10).
Plugging these values into the formula, we get:
A = 100,000(1 + 0.045/2)^(2*10)
Now let's calculate it step by step:
Step 1: Calculate the rate per period
Rate per period = annual interest rate / number of compounding periods per year
Rate per period = 0.045 / 2 = 0.0225
Step 2: Calculate the total number of compounding periods
Total number of compounding periods = number of compounding periods per year * number of years
Total number of compounding periods = 2 * 10 = 20
Step 3: Calculate (1 + rate per period) raised to the power of total number of compounding periods
(1 + 0.0225)^20 ≈ 1.550671
Step 4: Multiply the principal amount by the result from step 3
A = 100,000 * 1.550671 ≈ $155,067
So after 10 years, there will be approximately $155,067 in the account.