An investor who was not as astute as he believed invested $276,500 into an account 9 years ago. Today, that account is worth $213,600. What was the annual rate of return on this account

-2.83%

Explanation:

Given that

n = 9 years

Present value = 276500

Future value = 213600

Since

FV = PV (1 + r) ^n

213600 = 276500 (1 + r) ^9

Therefore

r = (213600/276500) ^1/9 - 1

r = (0.7725) ^1/9 - 1

r = 0.9717 - 1

r = - 0.0283 or - 2.83%

The annual rate of return is - 2.83%

Explanation:

The annual rate can be calculated from the formula FV=PV * (1+r) ^N

Where FV is the future value of the investment

PV is the amount invested which is $276,500

N is 9 years

213600=276,500 * (1+r) ^9

213600/276500 = (1+r) ^9

divide index on both sides by 9

(213600/276500) ^1/9=1+r

(213600/276500) ^1/9-1=r

r=-0.02827109

r=-2.83%

Hence the annual rate of return on the investment is - 2.83%, which means the investment depleted by 2.83% from initial invested amount of $276,5000 to $213,600 after nine years