Question

1. Calculate the present value of $500 annual investment for 5 years at 6% effective annual rate of return.

1. if investment is done at the end of each year
2. if investment is done at the beginning of each year

Answer 1

1. When the payment is made at the end of each year, it is called as ordinary annuity

Present value of annuity = C * [(1-(1+R)^-N)/R]

Where, C = Payment per period

R = Interest rate per period

N = Number of periods

So, Present value of annuity = 500 * [(1-(1+6%)^-5)/6%

= 500 * [(1-(1.06)^-5)]/0.06

= 500 * [( 1 - 0.74725817286)/0.06

= 500 * 4.21236378567

= 2106.18189283

So, the present value of annuity when the payment is made at the end is $2106.18189283

2. When the payment is made at the end of each year, it is called as annuity due

Present value of annuity = C * [(1-(1+R)^-N)/R] * (1+R)

So, Present value of annuity due = 500 * [(1-(1+6%)^-5)/6% * (1+6%)

=500 * [(1-(1.06)^-5)]/0.06 * (1.06)

= 500 * [( 1 - 0.74725817286)/0.06 * (1.06)

= 500 * 4.21236378567 * (1.06)

= 2232.55280641

So, the present value of annuity when the payment is made at the beginning is $2232.55280641