How much will be in the account after 4 years, if K5000 is invested into and account bearing 9% p.a. compounded monthly and after this first investment a further K300 is paid into that account at the end of every month
To calculate the future value of the investment after 4 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (K5000)
r = the annual interest rate (9% or 0.09)
n = the number of times interest is compounded per year (12 for monthly)
t = the number of years (4)
First, we calculate the monthly interest rate:
Monthly interest rate = annual interest rate / number of compounding periods per year
Monthly interest rate = 0.09 / 12
Monthly interest rate = 0.0075
Now, we calculate the future value of the initial K5000 investment after 4 years:
A1 = 5000(1 + 0.0075)^(12*4)
A1 = 5000(1.0075)^48
A1 = 5000 * 1.4197
A1 = K7098.50
Next, we calculate the future value of the monthly payments:
We can treat the monthly deposits as annuities and use the future value of an annuity formula:
FV = Pmt * (((1 + r/n)^(nt) - 1) / (r/n))
Where:
FV = future value of the annuity
Pmt = monthly payment (K300)
r = monthly interest rate (0.0075)
n = number of times interest is compounded per year (12)
t = number of years (4)
FV = 300 * (((1 + 0.0075)^48 - 1) / 0.0075)
FV = 300 * (1.4197 - 1) / 0.0075
FV = 300 * 209.23
FV = K62769
Finally, we add the future value of the initial investment and the future value of the monthly payments:
Total future value after 4 years = A1 + FV
Total future value = K7098.50 + K62769
Total future value = K69867.50
Therefore, after 4 years, the account will have a total of K69867.50 if K5000 is invested initially and an additional K300 is paid into the account at the end of every month.