You invest 250 per quarter for the next 30 years at an 8 ann

You invest $250 per quarter for the next 30 years at an 8% annual interest rate, starting today (beginning payment), compounded quarterly. How much are you going to have at the end of the 30^th year?

Solution

Solution: At the end of the 30th year value $124,505.83 Working Notes: Since investment are made at the beginning of period the quarter of years, to find the value of the investment at the end of 30 years , we have to find, Future value of annuity due Future value the payments are an annuity due Future value of annuity due= P x ((1+i)^n - 1) (1+i)/i P= investment per quarter =$250 i=interest rate per quarter = r%/4=8%/4 =2% = 0.02 n= no. Of period= no of year x no of quarter in a year n= 30 x 4 = 120 Future value of annuity due at t=30 = P x ((1+i)^n - 1) (1+i)/i Future value of annuity due at t=30 = 250 x ((1+0.02)^120 - 1) (1+0.02)/0.02 =$124,505.8287 =$124,505.83 Please feel free to ask if anything about above solution in comment section of the question.