use compound interest formula A=A0(1+r/n)nt. Suppose periodic deposits, of $P, a

Question

use compound interest formula A=A0(1+r/n)nt. Suppose periodic deposits, of $P, are made to an account ntimes per year with an APR of 'r' for 't' years.

1. Express the future value of this annuity as an infinitesum, then determine a closed form formula.

2. Using the result obtained above, derive the payment formulafor determining the amount of each payment (with n payments/year)one would make for barrowing $A with an APR of 'r' for 't'years.

use compound interest formula A=A0 (1 +r/n) nt. Suppose periodic deposits, of $P, are made to an account ntimes per year with an APR of r' for 't' years. 1. Express the future value of this annuity as an infinitesum, then determine a closed form formula. 2. Using the result obtained above, derive the payment formulafor determining the amount of each payment (with n payments/year)one would make for barrowing SA with an APR of 'r' for t'years

Explanation / Answer

Answer;

1. Future value of annuity

Closed form:

Future value of annuity =

2) By simply solving the above equation for P =

P = $A / [{(1+r)n-1}/ r] (ans)

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