Mr X deposit $3000 at the end of each semiannual period for 21 years at 8% interest compounded semiannually.Find the amout will have on deposit?
To calculate the amount Mr. X will have on deposit after 21 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $3000 (the amount deposited at the end of each semiannual period)
r = 8% = 0.08 (the annual interest rate)
n = 2 (compounded semiannually)
t = 21 (the number of years)
So, plugging these values into the formula, we have:
A = $3000(1 + 0.08/2)^(2*21)
Now, let's solve this equation step by step:
Step 1: Calculate the value inside the parentheses
(1 + 0.08/2) = 1 + 0.04 = 1.04
Step 2: Calculate the exponent
(2*21) = 42
Step 3: Calculate the final amount
A = $3000 * (1.04)^42
Using a calculator or spreadsheet, we can find the value of (1.04)^42 = 4.885228222
Finally, multiplying this value by the initial deposit, we get:
A = $3000 * 4.885228222 = $14,655.68
Therefore, Mr. X will have approximately $14,655.68 on deposit after 21 years.