Question #206412

the national bank give a prize of 1000000 L.E.your prize can be taken either in the form 40000 L.E at the end of each of the next 25 years or as a lump sum of 500000 L.E paid immdiately.

If you expect to be able to earn 5.5 percent annually on your investments over the next 25 years, which alternative should you take? why?

Expert's answer

**Solution:**

To determine the present value of annuity, we use the following formula:

"P[\\frac{1 - (1+r)^{-n} }{r} ]"

"= 40,000[\\frac{1 - (1+0.055)^{-25} }{0.055} ] = 40,000\\times 13.41 = 536,400"

PVA = 536,400 L.E

Gain = 536,400 - 500,000 = 36,400

I will take the second alternative since I will earn 36,400 L.E more compared to the lump sum amount being paid immediately. That is, the gain will be more if I receive annual payments for 25 years.

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