Use this formula to find A:
A = PR^n -[Q (R^n - 1)/(R - 1).
Use the following information to find A:
P = K15 000
Q = K250
Interest rate p.a. = 8.5%
Compounded = Quarterly
Years = 10
First, we must convert the interest rate to a quarterly rate by dividing 8.5% by 4 (since it is compounded quarterly).
Quarterly interest rate = 8.5%/4 = 2.125%
Next, plug all the values into the formula:
A = 15,000 * (1 + 0.02125)^40 - [250 * ((1 + 0.02125)^40 - 1) / 0.02125]
A = 15,000 * (1.02125)^40 - [250 * ((1.02125)^40 - 1) / 0.02125]
A = 15,000 * 2.04559835845 - (250 * 1.96168888387) / 0.02125
A = 30,683.9753777 - 11,615.448075 / 0.02125
A = 19,068.5273027 / 0.02125
A ≈ K895,941.67
Therefore, A is approximately K895,941.67.
If the interest rate p.a. is 8.5%, then R = 1 + (8.5/100). Now solve for A
Given:
P = K15,000
Q = K250
Interest rate p.a. = 8.5%
Compounded = Quarterly
Years = 10
First, we need to calculate the quarterly interest rate based on the annual rate of 8.5%:
R = 1 + (8.5 / 100)
R = 1 + 0.085
R = 1.085
Next, plug the values into the formula to find A:
A = 15,000 * (1.085)^40 - [250 * ((1.085)^40 - 1) / (1.085 - 1)]
A = 15,000 * 2.45838919774 - [250 * (2.45838919774 - 1) / 0.085]
A = 36,875.8389661 - [250 * 1.45838919774 / 0.085]
A = 36,875.8389661 - 4,232.84808025
A ≈ K32,643.99
Therefore, the value of A is approximately K32,643.99.
How did you get 2.45838919774
I apologize for the error in my previous response. Let's correct that calculation.
Given:
P = K15,000
Q = K250
Interest rate p.a. = 8.5%
Compounded = Quarterly
Years = 10
First, we need to calculate R:
R = 1 + (8.5 / 100)
R = 1 + 0.085
R = 1.085
Next, we plug the values into the formula to find A:
A = 15,000 * (1.085)^40 - [250 * ((1.085)^40 - 1) / (1.085 - 1)]
A = 15,000 * 2.22675234739 - [250 * (2.22675234739 - 1) / 0.085]
A = 33,401.785211 - [250 * 1.22675234739 / 0.085]
A = 33,401.785211 - 3,589.54365615
A ≈ K29,812.24
Therefore, the corrected value of A is approximately K29,812.24. Thank you for pointing out the error.