+0  
 
0
528
4
avatar+598 

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
edited by michaelcai  Sep 17, 2017
 #1
avatar
+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
avatar
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
 #3
avatar+598 
0

I figured it out

 

Edit: 63 was correct

michaelcai  Sep 17, 2017
edited by michaelcai  Sep 17, 2017
 #4
avatar
-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

23 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.