Question

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,750 at the end of Year 4 if the interest rate is 5%?

Answer 1

This question uses two applications of time value of money for 2 stream of funds or payments.

First stream is an ordinary annuity of $2,250 for 4 years at interest rate of 5%.

Second is a lump sum payment of $3,750 at 4^th year for same interest rate.

So, here we need to calculate the present values (at time t=0, i.e. today) of both the streams, and then add the two to get total value.

For the first stream of payment, let us calculate present value first

PV of an annuity is mathematically expressed as:

PV of an ordinary annuity with r = 5%, n = 4 years and P = $2,250 is

PV = $7,978.39

PV of annuity stream is hence = $7,978.39 ----------------------------- Value 1

For the second stream of payment, we would use the basic time value of money function, which is expressed as:

FV = PV * (1 + r)ⁿ

PV = 3750/(1 + 5%)⁴

PV = $3,085.13

PV of lump sum payment = $3,085.13……………………....Value 2

Total present value, hence = value 1 + value 2 = $7978.39 + $3085.13 = $11,063.52