Using the formula for PV (present value) of an oridinary annuity or the amortization formula to solve this problem.
PV=13000 I=.03% PMT=500 n=?
I have done it over and over and can't it correct
I got .03%
Thanks but sorry it was incorrect.
To solve this problem using the formula for present value (PV) of an ordinary annuity or the amortization formula, we can follow these steps:
1. The formula to find the present value of an ordinary annuity is: PV = PMT * [(1 - (1 + I)^(-n))/I]
In this formula:
- PV represents the present value (unknown in this case)
- PMT represents the payment made at each period ($500)
- I represents the interest rate per period (0.03% per period, which needs to be converted to a decimal by dividing it by 100, so I = 0.0003)
- n represents the total number of periods (unknown in this case)
2. Plug in the known values into the formula: PV = 13000, I = 0.0003, PMT = 500
3. The formula becomes: 13000 = 500 * [(1 - (1 + 0.0003)^(-n))/0.0003]
4. Rearrange the equation to isolate (1 - (1 + 0.0003)^(-n)): (1 - (1 + 0.0003)^(-n)) = (13000 * 0.0003) / 500
5. Simplify the right side of the equation: (1 - (1 + 0.0003)^(-n)) = 7.8
6. Take the natural logarithm (ln) of both sides of the equation to eliminate the exponent:
ln(1 - (1 + 0.0003)^(-n)) = ln(7.8)
7. Solve for n by finding the inverse of the exponent: -n = ln(7.8) / ln(1 + 0.0003)
8. Calculate the value of -n using a scientific calculator: -n = ln(7.8) / ln(1.0003)
9. Finally, multiply -n by -1 to find the positive value of n: n ≈ -(-8.308)
10. The approximate value of n, the total number of periods, is 8.308 (rounded to three decimal places).
Therefore, solving the problem using the formula for present value (PV) of an ordinary annuity or the amortization formula, the total number of periods (n) is approximately 8.308.