Question

You're prepared to make monthly payments of $320, beginning at the end of this month, into an account that pays 8 percent interest compounded monthly. How many payments will you have made when your account balance reaches $20,263?

Answer 1

Future value = $ 20,263

Monthly depsoit = $ 320 payment at end of each month.

interest rate = 8% compounding monthly

Future value = Periodic deposit *[ ( 1 + i / k)n*k - 1 ] / (i/k)

20,263 = 320 * [ (1 + 0.08 / 12)n*12 - 1 ] / (0.08/12)

20,263 * 0.006667 = 320 * [(1.006667)12n  - 1]

135. 093421 / 320 = ( 1.006667)12n - 1

(1.006667)12n = 1.422166940625

Apply log on both sides

Log (1 .006667)12n = Log(1.422166940625)

12n Log(1.006667) = Log(1.422166940625)

12n = Log(1.422166940625) / Log(1.006667)

12n = 0.1529505789 / 0.00288583204

12n = 53.000513

Here 12n means number of deposits

Here 53 payments will you have made when your account balance reaches $ 20,263