Question

If Haley invests $1,000 at the end of every month (EOM) for seven years in an investment paying an annual rate of 10% compounded monthly, how much will she have at the end of seven years?

If Haley invests $1,000 at the beginning of every month (BOM) for seven years in an investment paying an annual rate of 10% compounded monthly, how much will she have at the end of seven years?

Answer 1

The amount Haley will have at the end of seven years will be the Future value of annuity. Annuity is a series of payments made at regular intervals.

1. If Haley invests $1,000 at the end of every month (EOM)

This is an ordinary annuity because the investment is made at the end of each period.

The formula to compute Future value of ordinary annuity is:

FV of Ordinary Annuity = P [ ( (1+r/n)^nt - 1 ) / (r/n) ]

P = Periodic payments = 1000

r = Rate of interest = 10% ie,0.10

n = Compounding frequency per period = 12

t = Number of years = 7

Substituting the values in the formula we get,

= 1000 [ ( (1 + 0.10/ 12)^12*7 - 1 ) / (0.10/12)

= 1000 [ ( (1 + 0.008333)⁸⁴ - 1 ) / 0.0083333 ]

= 1000 [ ( 1.008333⁸⁴ - 1 ) / 0.0083333 ]

= 1000 [ ( 2.007914 - 1 ) / 0.0083333 ]

= 1000 [ 1.007914 / 0.0083333 ]

= 1000 * 120.95016

= 120,950

Therefore, the amount she will have at the end of seven years is $120,950

2. If Haley invests $1,000 at the beginning of every month (BOM)

This is an annuity due because the investment is made at the beginning of each period.

The formula to compute Future value of annuity due is:

FV of Annuity Due = FV of Ordinary Annuity * (1 + r/n)

= 120950 * ( 1 + 0.10/12 )

= 120950 * 1.0083333

= 121,958

Therefore, the amount she will have at the end of seven years is $121,958