Question

Ali wants to accumulate 150,000 dollars at the end of year 12 .To do this he will deposit 10 equal annual amounts starting from end of year 1 . the bank have an interest   rate of 10% per year . what is the magnitude of the annual payments ? .

Answer 1

Let the annual payment is $X and there is 10 equal payments. If there is 10 equal payments starting from end of year 1 the Present value of those annual payment i.e the value of those annual payment at year - '0' will be -

$X*(P/A, 10%, 10)

= $X*[{(1+0.1)^10 - 1}/{0.1(1+0.1)^10}]

= $X*6.14456

Now future value after 12 years of this present value can be calculated as follows -

$X*6.14456*(F/P, 10%, 12)

This value will be equivalent to $150,000 which Ali wants to get after 12 years. Therefore we can write it as follows -

X*6.14456*(F/P, 10%, 12) = $150,000

Or, X*6.14456*(1+0.1)^12 = $150,000

Or, X*6 .14456*3.1384 = $150,000

Or, X*19.284 = $150,000

Or, X = $150,000/19.284 = $7,778.46

So, the magnitude of annual payment is $7,778.46 (Answer).