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.
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
1 answer
1 answer