Question

You have $50,000 in savings for retirement in an investment earning a stated annual rate of 7% compounded monthly. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth. Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.

Answer 1

C.I = Principal*(1+i/m)^(n*m) ---------------------------------------(A)

Where C.I Compounding Interest = $ 1000000

Principal Amt. = 50000

Rate of interest (i) = 7%

Compounding monthly = 12 times in a year

Now put all the values in above equation (A)

1000000 = 50000*(1+0.07/12)^(n*12)

1000000/50000 = (1.005833)^(12*n)

20 = 1.005833^(12*n)

Take log of both sides

log(20) = log(1.005833)^(12*n) -------log m^n = nlogm

2.996043 = 12n*0.005817

12n = 2.996043/0.005817

n = 2.996043/(0.005817*12)

n = 42.92 Years

or 42 Years,11 Months & 2days (approx.) {0.92*12 = 11.04 months & 0.04*30 = 1.2 days}

Please check with your answer and let me know.