Question

You agree to deposit $500 at the beginning of each month into a bank account for the next 24 months. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what annual interest rate will you have earned?

Note: Only use the formula listed and show the steps of how you reached the answer, I don't need to know just the answer, I'm trying to learn. Thank you. Don't use excel.

01POPO TABLE 5-7 Summary of Time Value of Money Equations Calculation Equation Future value of a single payment FV, = PV(1 + ) Present value of a single payment "L(1 + 0"] Future value of an annuity [(1 + A" – 1] FV of an annuity = PMT PV=Fyl 1 Present value of an annuity 1 – (1 + nan PV of an annuity = Php 1 - 4, + PV of an annuity 1] Future value of an annuity due Present value of an annuity due Effective annual rate (EAR) FV,(annuity due) = future value of an annuity X (1 + n) Pannuity due) = present value of an annuity x (1 + n) APR or quoted annual rate EAR = 1 + compounding periods per year (m) APRn Future value of a single payment with nonannual compounding PVI 1 + Present value of a perpetuity PV = PP Notations: FV, = the future value of the investment at the end of n years n= the number of years until payment will be received or during which compounding occurs p= the annual interest or discount rate PV = the present value of the future sum of money m= the number of times compounding occurs during the year PMT = the annuity payment deposited or received at the end of each year PP = the constant dollar amount provided by the perpetuity

Answer 1

Answer:

Given

Monthly deposit D=500

Number of payment N=24

Amoutn recived after 24th month A=13000

Since amount is deposited at beginning of month so it is annuity due problem

Let r be the monthly interest rate

A=D*(1+r)*((1+r)^N-1)/r

13000=500*(1+r)*((1+r)^24-1)/r

Solving for r we get r =0.69%

So annual interest rate =12*r=12*0.69%=8.26%