Question

1) You wish to accumulate $100,000 through monthly payments of $100. If you can earn interest at an annual rate of 4% compounded monthly, how long (to the nearest year) will it take to accomplish your goal?
________  yr

2)Alonzo plans to retire as soon as he has accumulated $250,000 through quarterly payments of $3,500. If Alonzo invests this money at 5.4% interest, compounded quarterly, how long (to the nearest year) until can he retire?
_____ year

3) Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,700 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much will you receive each quarter? (Round your answer to the nearest cent.)
$ _______

4). You wish to accumulate $100,000 through monthly payments of $100. If you can earn interest at an annual rate of 4% compounded monthly, how long (to the nearest year) will it take to accomplish your goal?
_________ yr

5) Alonzo plans to retire as soon as he has accumulated $250,000 through quarterly payments of $3,500. If Alonzo invests this money at 5.4% interest, compounded quarterly, how long (to the nearest year) until can he retire?
________ yr

PLEASE help ! GBU

Answer 1

1). The future value (F) of an annuity is given by F = (P/r)[(1+r)ⁿ-1], where P is the periodic payment , r is the rate per period and n is the number of periods.

Here, F = 100000, P = 100 and r = 0.04. Therefore, 100000 = (100/0.04)[ (1.04)ⁿ-1] or, (1.04)ⁿ-1 = 100000*0.04/100 = 40 so that (1.04)ⁿ = 40+1= 41.

Now, on taking log of both the sides, we get n log 1.04 = log 41 so that n = log 41/log 1.04 = 1.612783857/0.017033339 = 94.68 say 95 ( on rounding off to the nearest whole number).

Thus, it will take 95 months or, 8 years ( on rounding off to the nearest year) to accumulate $ 100000.

2). The future value (F) of an annuity is given by F = (P/r)[(1+r)ⁿ-1], where P is the periodic payment , r is the rate per period and n is the number of periods.

Here, F = 250000, P = 3500 and r = 5.4/400 = 0.0135. Therefore, 250000 = (3500/0.0135)[ (1.0135)ⁿ-1] or, (1.0135)ⁿ-1 = 250000*0.0135/3500 = 27/28 so that (1.0135)ⁿ = 27/28 +1= 55/28.

Now, on taking log of both the sides, we get n log 1.0135 = log (55/28)= log 55-log 28.

Hence n = (log 55-log 28)/log 1.0135 = 0.293204658/0.005823753029 = 50.35( approximately).

Thus, it will take 50.35 quarters or, 50.35/4 = 12.59 years , say 13 years ( on rounding off to the nearest years).

Please post the remaining questions again, one at a time.