An engineer invested $\$10,\!000$ in a six-month savings certificate that paid a simple annual interest rate of $12\%$. After six months, she invested the total value of her investment in another six-month certificate. After six more months, the investment was worth $\$11,\!130$. What was the annual interest rate of the second certificate?

michaelcai
Sep 17, 2017

#1**+1 **

This is the formula you would use to compare the 2 investments:

FV = PV x [1 + R]^N

FV =$50,000 x [1 + 0.04]^2

FV =$50,000 x 1.0816

FV =$54,080 - Jose's investment.

FV =$50,000 x [1 + 0.04/4]^(2*4)

FV =$50,000 x 1.01^8

FV =$50,000 x 1.0828567056280801

FV =$54,142.84 - Patricia's investment.

**$54,142.84 - $54,080 =~$63 - extra that Patricia's investment earned.**

Guest Sep 17, 2017

#2**0 **

What happened to your Jose's and Patricia's question that I just answered? Did you delete it and why?

Guest Sep 17, 2017

#4**-1 **

$10,000 x [12%] / 2 =$10,000 x 0.06 =$600 interest earned for the 1st 6 months.

$10,000 + $600 =$10,600 principal + interest for the 1st 6 months.

$11,130 / $10,600 =1.05

[1.05 -1] x 100 =**5% This is the effective annual interest on the 2nd certificate. Or you can:**

1.05^1/2 =[1.0246950 - 1] x 100=2.4695% semi-annual copound rate. Or:

2.4695 x 2 =**4.939% - This is called** **nominal annual rate compounded semi-annually, which is equivalent to 5% effective annual rate.**

Guest Sep 17, 2017

edited by
Guest
Sep 17, 2017