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 solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case, John saves $10,000 every semester (twice a year), so the principal investment amount (P) is $10,000.
The annual interest rate (r) is 10% or 0.10 (decimal).
The interest is compounded semiannually, so the number of times that interest is compounded per year (n) is 2.
And the time period (t) is 1.5 years.
Let's substitute these values into the formula and calculate the future value (A):
A = 10000(1 + 0.10/2)^(2*1.5)
A = 10000(1 + 0.05)^3
A = 10000(1.05)^3
A = 10000 * 1.157625
A ≈ $11,576.25
Therefore, John will redeem approximately $11,576.25 after 1.5 years, compounded semiannually at the end of each semester.