Question

You are in a dispute with your bank over the interest you have accrued. You deposited $1000, 7 years ago, and now have a balance of exactly $2000 which makes a 7 year holding rate of return of 100%. The banker, confusing average rate of return with annualized rate of return, claims you have earned an annualized rate of return of 14.286%. Being a shrewd student, calculate the correct annualized rate of return, and compute how much money you would have had if you'd indeed earned the average rate of return (14.286%) for 7 years. Report the value (B / A), where B is how much money you would have had, and A is the correct rate of return (in decimal format). Note: this ratio doesn't carry any special meaning; it's just an easy way for me to check two answers at the same time.

Answer 1

USing the financial calculator

Input PV = -1000, FV =2000, N =7

Find I/Y as 10.41%

Thus the annualized rate is 10.41%

If the rate was 14.286% the value after 7 years would be

FV= PV*(1+r)^n

=1000*1.14286^7

=$2546.544

B/A = 2546.544/ 0.1041 = 24462.48