# Thread: annuity present value problem: why is interest rate converted to monthly?

1. ## annuity present value problem: why is interest rate converted to monthly?

Can anyone please explain why the interest rate (in the solution to the example at the bottom of this page) is converted into monthly while it already says 15% compounded monthly?

Example 2.7

. . .A principal of $50,000 is to be borrowed at an interest rate of 15% compounded monthly for 30 years. What will be the monthly payment to repay the loan? . . .Solution: Monthly interest i = 0.15/12 = 0.0125, or 1.25%. Since Appendix A does not contain a table for that interest rate, one must use the formulas. . . . . .$A\, =\, P\, (A/P)_{i,n}\, =\, 50000\, (A/P)_{1.25, 360}$ . . . .. . .$=\, 50000\, \cdot\, \dfrac{(0.0125)\, (1\, +\, 0.0125)^{360}}{(1\, +\, 0.0125)\, -\, 1}$ . . .. . . .$=\, 50000\, (0.012644)\, =\, \632$ in my mind i have A = P(A/P,i,n); i = 15%, n = 360 but solution is different here 2. Originally Posted by Tayeeba Can anyone please explain why the interest rate (in the solution to the example at the bottom of this page) is converted into monthly while it already says 15% compounded monthly? Example 2.7 . . .A principal of$50,000 is to be borrowed at an interest rate of 15% compounded monthly for 30 years. What will be the monthly payment to repay the loan?

. . .Solution: Monthly interest i = 0.15/12 = 0.0125, or 1.25%. Since Appendix A does not contain a table for that interest rate, one must use the formulas.

. . . . .$A\, =\, P\, (A/P)_{i,n}\, =\, 50000\, (A/P)_{1.25, 360}$

. . . .. . .$=\, 50000\, \cdot\, \dfrac{(0.0125)\, (1\, +\, 0.0125)^{360}}{(1\, +\, 0.0125)\, -\, 1}$

. . .. . . .$=\, 50000\, (0.012644)\, =\, \632$

in my mind i have A = P(A/P,i,n); i = 15%, n = 360
but solution is different here
Not clear in the problem, but meant was 15% APR
compounded monthly: so 15/1200 = .0125 = I

Formula is P = Ai / [1 - 1/(1+i)^n]
A = amount borrowed (50000)
i = monthly interest factor (.0125)
n = number months (360)
P = monthly payment (?)

3. Originally Posted by Denis
Not clear in the problem, but meant was 15% APR
compounded monthly: so 15/1200 = .0125 = I

Formula is P = Ai / [1 - 1/(1+i)^n]
A = amount borrowed (50000)
i = monthly interest factor (.0125)
n = number months (360)
P = monthly payment (?)
Thanks Denis, got it

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