Use this formula A =PR^(n) - [(Q(R^(n) - 1))/(R - 1)] to find A.
Where:
P = K15000
Q = K250
R = 1.085
It is compounded quarterly in 10 years.
First, we need to calculate the value of n. Since the compounding is done quarterly over 10 years, there will be a total of 4 compounding periods per year for 10 years.
n = 4 * 10 = 40
Now we can plug in the values of P, Q, R, and n into the formula to calculate A.
A = 15000 * 1.085^(40) - [(250 * (1.085^(40) - 1))/(1.085 - 1)]
A = 15000 * 11.024 - [(250 * 11.024 - 1)/(0.085)]
A = 165360 - (2756.21 / 0.085)
A = 165360 - 32478.35
A = 132881.65
Therefore, the value of A after 10 years will be K132881.65.
The correct answer is K391699.5512
I apologize for the mistake. Let me correct the calculation:
A = 15000 * 1.085^(40) - [(250 * (1.085^(40) - 1))/(1.085 - 1)]
A = 15000 * 11.024 - [(250 * 11.024 - 1)/(0.085)]
A = 165360 - (2756.21 / 0.085)
A = 165360 - 32478
A = K132882
I apologize for the incorrect calculation. Thank you for pointing that out.
For the original question the interest rate p.a. is 8.5%. Now redo the question
Given that the interest rate is 8.5% per annum, we need to convert this annual interest rate into a quarterly interest rate for compounding quarterly.
Quarterly interest rate = (1 + 0.085/4) = 1.02125
Now, we can plug in the new quarterly interest rate into the formula to calculate A.
A = 15000 * 1.02125^(40) - [(250 * (1.02125^(40) - 1))/(1.02125 - 1)]
A = 15000 * 2.72325 - [(250 * 2.72325 - 1)/(0.02125)]
A = 40848.75 - (53.82 / 0.02125)
A = 40848.75 - 2531.76
A = K38316.99
Therefore, the value of A after 10 years with an 8.5% annual interest rate compounded quarterly is K38316.99.