If john saves 10000 every semester in a bank a/c which pays 10%. How much will he redeem after 1.5 years compounded semiannually at the end of semester.
To calculate the amount that John will redeem after 1.5 years, we need to consider the compounded interest on his savings.
First, we need to determine the number of compounding periods. Since the interest is compounded semiannually, there will be 3 compounding periods over the 1.5-year period (each semester has one compounding period).
Next, we need to calculate the interest rate per compounding period. The annual interest rate is 10%, so the semiannual interest rate is half of that, which is 5%.
We can now apply the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the amount after time t
P = the principal amount (initial savings)
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = time in years
In this case, John's initial savings (P) is $10,000, the semiannual interest rate (r) is 5%, the number of compounding periods per year (n) is 2 (since interest is compounded semiannually), and the time (t) is 1.5 years.
Plugging in these values into the formula, we have:
A = $10,000(1 + 0.05/2)^(2*1.5)
A = $10,000(1.025)^3
A ≈ $10,000(1.076890625)
A ≈ $10,768.91
Therefore, John will redeem approximately $10,768.91 after 1.5 years compounded semiannually at the end of each semester.