Answer:
We can use the formula for compound interest to calculate the amount that Modise will receive after 12 years:
A = P(1 + r/n)^(nt)
where:
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = 20,000, r = 0.09 (9% expressed as a decimal), n = 1 (compounded annually), and t = 12. Plugging these values into the formula, we get:
A = 20,000(1 + 0.09/1)^(1*12)
= 20,000(1.09)^12
= 20,000(2.367)
= 47,340
Therefore, Modise will receive an amount of R47,340 after 12 years.
To calculate the amount of interest earned, we can subtract the initial investment from the total amount received:
Interest = A - P
= 47,340 - 20,000
= 27,340
Therefore, Modise earned R27,340 in interest over the 12-year period.