A company wants to accumulate tsh 100000 to purchase replacement machinery 8years from know.to accomplish this equal semi-annually payments are made to a fund that earns 7%compounded semi-annually.find the amount of each payment
let the payment be P
P (1.035^16 - 1)/.035 = 100000
solve for P on your calculator
you should get around ($4770 , not the exact answer so you will still have to do the calculation yourself)
To find the amount of each semi-annual payment, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (desired amount of TSH 100,000)
P = Payment amount
r = Interest rate per compounding period (7% per compounding semi-annually)
n = Number of compounding periods (8 years, which is 16 semi-annual periods)
Now, let's plug in the values into the formula and solve for P:
100,000 = P * [(1 + 0.07/2)^(16) - 1] / (0.07/2)
First, let's simplify the equation a bit:
100,000 = P * (1.035^16 - 1) / 0.035
Now, we calculate the value inside the brackets:
1.035^16 ≈ 1.68043
So, the equation becomes:
100,000 = P * (1.68043 - 1) / 0.035
Now, let's simplify further:
100,000 = P * 0.68043 / 0.035
Next, we isolate P by multiplying both sides by 0.035:
3,500 = P * 0.68043
Finally, divide both sides by 0.68043 to solve for P:
P ≈ 5,138.20
Therefore, the amount of each semi-annual payment would be approximately TSH 5,138.20.