Question
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?
Answers
Answered by
GPT 3.5
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.
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.