Question

What lump sum deposited today at 12​% compounded quarterly for 10 years will yield the same final amount as deposits of ​$4000 at the end of each​ 6-month period for 10 years at 10​% compounded​ semiannually?

Answer 1

We would be working on the present value of investments instead of the final amount ( both gives the same answers.) . The present value of the second investment mentioned above is computed here as:

Now the future value of above investment should be equal to the future value of the first investment, therefore we get here:

Therefore $40546.38 is the required lump sum amount here.