Question
A principal of R1 700.00 is invested for 2.5 years at a rate of 6.5% per annum compounded quarterly. Determine what the investment will amount to at the end of the term and how much interest will be earned.
Answers
Answered by
GPT 3.5
First, we need to calculate the interest earned for each quarter using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (R1 700.00 in this case).
r = annual interest rate (6.5%).
n = number of times the interest is compounded per year (4 for quarterly).
t = number of years the money is invested for (2.5 years).
Calculating the interest earned for each quarter:
r = 6.5% = 0.065
n = 4
t = 2.5
A = R1 700.00(1 + 0.065/4)^(4*2.5)
A = R1 700.00(1 + 0.01625)^10
A = R1 700.00(1.01625)^10
A = R1 700.00(1.17264060085)
A = R1 997.48
The investment will amount to R1 997.48 at the end of the term.
Now, calculate the interest earned:
Interest = A - P
Interest = R1 997.48 - R1 700.00
Interest = R297.48
Therefore, the interest earned will be R297.48.
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (R1 700.00 in this case).
r = annual interest rate (6.5%).
n = number of times the interest is compounded per year (4 for quarterly).
t = number of years the money is invested for (2.5 years).
Calculating the interest earned for each quarter:
r = 6.5% = 0.065
n = 4
t = 2.5
A = R1 700.00(1 + 0.065/4)^(4*2.5)
A = R1 700.00(1 + 0.01625)^10
A = R1 700.00(1.01625)^10
A = R1 700.00(1.17264060085)
A = R1 997.48
The investment will amount to R1 997.48 at the end of the term.
Now, calculate the interest earned:
Interest = A - P
Interest = R1 997.48 - R1 700.00
Interest = R297.48
Therefore, the interest earned will be R297.48.