You set up an annuity in which you will pay $150 per month for 20 years at 7 per cent annual interest.
What is the total amount this will yield in 20 years?

Using the formula above, the easiest amount to find is the monthly amount of $150.
For the interest rate ‘r’, we have to convert it from annual to monthly.
.07 ÷ 12 = 0.0058333333 per month.
Since this is a monthly annuity, we have to change the time from years to months.
20 years = 240 months.
Now we put these amounts into the formula:
Total = 150 • ([1.0058333333²⁴¹ -1] ÷ .00375) – 150
Total = 150 • ([4.0622981589 -1] ÷ .00375) -150
Total = 150 • (3.0622981589 ÷ .00375) -150
Total = 150 • (524.9653986745) -150
Total = 78,594.81

You set up a pension plan with an annual interst rate of 8 per cent, for 35 years and you would like this to result in $1,000,000.00 for your retirement.
How much must you invest each month?

In this case, the easiest amount to find is the total which is $1,000,000. As in the previous example, we need to convert the interst rate to a monthly rate and convert the years into months.
8% per year = .08/12 = 0.0066666666 per month and
35 years = 420 months.

Entering the amounts into the above formula we have:
Monthly Amount = 1,000,000 ÷ [(1.0066666666⁴²¹ -1) ÷ (.0066666666) -1] Monthly Amount=1,000,000 ÷ [16.4011668971 -1
÷ (.0066666666) -1] Monthly Amount=1,000,000 ÷ [15.4011668971
÷ (.0066666666) -1] Monthly Amount = 1,000,000 ÷ (2,310.1750345608 -1);
Monthly Amount = 1,000,000 ÷ (2,309.1750345608);
Monthly Amount = 433.0550889531
Monthly Amount = 433.06

You decide to invest $250 per month in a 7.5% annual interest rate pension plan and you’d like to retire with $500,000.
How long will this take?

For this calculation. we need to use the monthly rate which is .075/12 = .00625.
First, we’ll enter these amounts:
(.00625) × (500,000 / 250) + (1.00625)
= 13.50625
Taking the logarithm of this and dividing it by the logarithm of the denominator:
Log (13.50625) ÷ Log(1.00625) =
1.1305347842 ÷ 0.0027058934 =
417.8046312859
Finally, the formula says we have to subtract 1 from this number:
416.8046312859 months
It takes this number of months to yield $500,000.
Dividing this by 12 yields
34.7337192738 years.