Find the interest earned for an investment if the accumulated amount at the end of 6 years is RM 2,412.66 and the interest rate given is 8% compounded quarterly.
To find the interest earned for this investment, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = accumulated amount at the end of the investment period
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
A = RM 2,412.66
r = 8% = 0.08 (as a decimal)
n = 4 (quarterly compounding)
t = 6 years
We can rearrange the formula to solve for the principal amount:
P = A / (1 + r/n)^(nt)
P = 2412.66 / (1 + 0.08/4)^(4*6)
P = 2412.66 / (1 + 0.02)^(24)
P = 2412.66 / 1.02^(24)
P = 2412.66 / 1.593848
P ≈ 1514.56
So, the principal amount (initial investment) is approximately RM 1,514.56.
To find the interest earned, we subtract the principal amount from the accumulated amount:
Interest Earned = A - P
Interest Earned = 2412.66 - 1514.56
Interest Earned ≈ 898.10
Therefore, the interest earned for this investment is approximately RM 898.10.
To find the interest earned for an investment, we need to calculate the principal amount first using the accumulated amount and the interest rate. Then, we can subtract the principal amount from the accumulated amount to get the interest earned.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, we are given the following information:
Accumulated amount (A) = RM 2,412.66
Interest rate (r) = 8% = 0.08 (as a decimal)
Number of times compounded per year (n) = 4 (quarterly)
Time (t) = 6 years
We need to find the principal amount (P) using this formula:
P = A / (1 + r/n)^(nt)
Calculating the principal amount:
P = 2412.66 / (1 + 0.08/4)^(4*6)
= 2412.66 / (1 + 0.02)^(24)
= 2412.66 / (1.02)^(24)
≈ 1,875.89
Now that we have the principal amount (P), we can calculate the interest earned:
Interest earned = Accumulated amount - Principal amount
= 2412.66 - 1875.89
≈ 536.77
Therefore, the interest earned for the investment is approximately RM 536.77.
P = Po(1+r)^n.
r = 0.08/4 = 0.02 = quarterly % rate.
n = 6*4 = 24 compounding periods.
P = 2412.66.
Po =
Int. = P-Po.
po =