A newly married couple decides to save R1 200 at the beginning of each month for 3 years, which they plan to use as a deposit on their first house. The account into which this money is deposited earns interest at a rate of 12% per annum, compounded monthly. How large a deposit will they have saved in three years?
To calculate the future value of the monthly deposits with compound interest, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (monthly deposit)
r = Annual interest rate (12%)
n = Number of times the interest is compounded per year (12 for monthly)
t = Number of years (3)
First, we need to calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12 = 0.12 / 12 = 0.01
Now we substitute the values into the formula:
FV = 1200(1 + 0.01)^(12*3)
FV = 1200(1.01)^36
FV = 1200(1.485947)
FV = 1783.1364
Therefore, the couple will have saved approximately R1 783.14 as a deposit on their first house after 3 years.