Question

1. Explain the difference between the present value of a lump sum investment and anannuity2.Explain the difference between the present value of an ordinary annuity and an annuitydue.3. Explain which variables would be included when using technology to calculate thepresent value of a lump sum and to calculate the present value of an annuity.

Answer 1

1. A lump sum is a one-time payment after a certain period of time, whereas an ordinary annuity involves equal installments in a series of payments over time. A business can use lump sum or ordinary annuity calculations for present value and future value calculations.

The present value of a lump sum is the value of the amount today

2. The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate.

Annuity due is an annuity whose payment is due immediately at the beginning of each period.

3. The present value of a lump sum is defined as:

`PV\text{ = }\frac{FV}{(1\text{ + i\rparen}^n}`

Where variables in the formula are explained as follows

PV = Present Value of the given amount today

FV = Future Value of the given amount

i = Discount rate

n = Number of periods

The Present value of an annuity is given as:

`P\text{ = PMT }*\text{ }(1-((1)/((1+r)^n)))/(r)`

The variables in the equation are explained as the follows:

P = the present value of annuity

PMT = Payment per period or the amount in each annuity payment

r = the interest or discount rate

n = total number of periods or the number of payments left to receive