Question

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

Answer 1

Answer:

-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%

Answer 2

Answer:

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