# Quantitative Meths - Schweser Wrong?

Question and answer from the Schweser Qbank below.

The following has me confused: i = 0.61761 × 12 = 7.411%???

Shouldn’t it be i = 0.61761 DIVIDED by 12 = 7.411% since the 35 years was multiplied by 12?

A recent ad for a Roth IRA includes the statement that if a person invests \$500 at the beginning of each month for 35 years, they could have \$1,000,000 for retirement. Assuming monthly compounding, what annual interest rate is implied in this statement? A) 7.411%. B) 7.625%. C) 6.988%. Your answer: C was incorrect. The correct answer was A) 7.411%. Solve for an annuity due with a future value of \$1,000,000, a number of periods equal to (35 × 12) = 420, payments = -500, and present value = 0. Solve for i. i = 0.61761 × 12 = 7.411% stated annually. Don’t forget to set your calculator for payments at the beginning of the periods. If you don’t, you’ll get 7.437%.

Their answer is correct. When you increase the number of periods to account for more frequent deposits, you get a per-period interest rate. In this case, the interest rate you solve for is monthly. You multiply by 12 to get the nominal annual interest rate. 0.61761% divided by 12 is certainly not even close to 7.411% anyway.

It’s the same like 0. 0** 0**61762 x12… Whole numbers are used for the %s instead of decimals. That’s why they get 7.411% rather than 0.07411 and the calculation is not wrong at all. I assume that confused you. Know the difference- 0.61=61%; 0.0061=0.61% On the other hand the division you mentioned makes no sense.

No.

0.61761% is the rate per month

you can write:

i = 0.61761% × 12 = 7.411%

or

i = 0.0061761 × 12 = 0.07411 = 7.411%