please - How do we manually calculate the Present Value of annuity step by step using this formula:
PV=R[1-(1+i)-n / i
for example:
PV = 2700[1-(1+.065)-4
___________________ = 9249.66
0.065
How did they get this answer (9249.66)?
I'm so lost. just to clarify too, -4 is an exponent. I couldn't change font for this to be apparent. Please a step by step answer would really help. Thank you in advance for your help, this site is such a wonderful service.
hoping you have a decent calculator with brackets, here are the keystrokes I did on my "Sharp"
1
-
(
1.065
yx , (you should have such a key)
4 ±
)
=
÷
.065
=
x
2700
=
I get 9249.66
If I could hug you I would. You have no idea how helpful this was, I can now proceed with the rest of the equations. Thank you kindly :)
To manually calculate the present value of an annuity using the formula PV=R[1-(1+i)^-n / i], where PV is the present value, R is the regular payment, i is the interest rate per period, and n is the number of periods, follow these steps:
Step 1: Identify the values given in the problem
In your example, the given values are:
R = 2700 (regular payment)
i = 0.065 (interest rate, which is equivalent to 6.5%)
n = 4 (number of periods)
Step 2: Plug in the values into the formula
Substituting the given values into the formula, we get:
PV = 2700[1-(1+0.065)^-4 / 0.065]
Step 3: Simplify the calculation inside the brackets first
Using the exponent operation first, we have:
PV = 2700[1-(1.065)^-4 / 0.065]
Step 4: Calculate the value inside the brackets
To calculate (1.065)^-4, raise 1.065 to the power of -4:
(1.065)^-4 = 0.8227 (rounded to four decimal places)
Step 5: Substitute the simplified value
Now, substitute the simplified value into the formula:
PV = 2700[1-0.8227 / 0.065]
Step 6: Perform the division inside the brackets
Divide 0.8227 by 0.065:
0.8227 / 0.065 = 12.6554 (rounded to four decimal places)
Step 7: Substitute the division result
Substitute the division result back into the formula:
PV = 2700[1-12.6554]
Step 8: Perform the subtraction inside the brackets
Subtract 12.6554 from 1:
1 - 12.6554 = -11.6554
Step 9: Calculate PV
Finally, multiply the regular payment (2700) by the result:
PV = 2700 * (-11.6554) = -31458.36 (rounded to two decimal places)
Therefore, the present value of the annuity is approximately -31458.36.