Thread: Simple and Compound Interest Problem

1. Simple and Compound Interest Problem

Hi All,

Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received$605 as interest. What was the value of his total savings before investing in these two bonds?

1. $5500 2.$ 11000
3. $22000 4.$ 2750
5. $44000 Answer Explanation... 1. Interest for the first year of the simple compound bond is 275/2 -$275.
2. So we need to determine the rate of interest based on this so...

605 - 550 = 55. That's the difference between the interest earned on the simple vs compound interest bonds.

55/275 * 100/1 = 11/55 * 100/1 = 20% Interest

3. 275 represents 20% interest of a number
275/20 * 100/1 = 55/4 * 100/1 = $1375. 4. This represents half the money so 1375*2 =$2750. (D).

My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)

2. Hello, dumluck!

I'm not impressed with their explanation.

Q: Shawn invested one half of his savings in a bond
that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, compounded annually, for the same 2 years at the same rate of interest and received$605 as interest.

What was the value of his total savings before investing in these two bonds?

. . $\displaystyle 1.\;\$5500 \qquad 2.\;\$11000 \qquad 3.\;\$22000 \qquad 4.\;\$2750 \qquad 5.\;\$44000$Let$\displaystyle \,r$be the annual interest rate for both accounts. Let$\displaystyle \,P$be the amount invested in each account. He invested$\displaystyle \,P$dollars at$\displaystyle \,r$percent simple interest for 2 years. . . This earned: .$\displaystyle P(r)(2) \:=\:2Pr$dollars in interest. So we have: .$\displaystyle 2Pr \:=\:550 \quad\Rightarrow\quad P \:=\:\dfrac{275}{r}$.[1] He invested$\displaystyle \,P$dollars at$\displaystyle \,r$percent compounded annualy for 2 years. . . This grew to: .$\displaystyle P(1+r)^2 $dollars in two years. His interest is: .$\displaystyle P(1+r)^2 - P \;=\;P\left[(1+r)^2 - 1\right] $dollars. . . So we have: .$\displaystyle P(2r + r^2) \:=\:605$.[2] Substitute [1] into [2]: .$\displaystyle \dfrac{275}{r}(2r + r^2) \:=\:605$. . . . . .$\displaystyle 2 + r \:=\:\dfrac{605}{275}\:=\:2.2 \quad\Rightarrow\quad r \:=\:0.2$Substitute into [1]: .$\displaystyle P \:=\:\dfrac{275}{0.2} \:=\:1375$Hence, he invested$\displaystyle \$1375$ in each account.

Therefore, he invested a total of $\displaystyle \$2750.\$

3. Originally Posted by dumluck
My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)
Code:
Simple interest:
0            1375.00
1   275.00   1650.00
2   275.00   1925.00
Compound interest:
0            1375.00
1   275.00   1650.00
2   330.00   1980.00
The 55 is the interest on the 275 (275 * .20 = 55) paid at end of 1st year
(in the compound interest case, of course); makes 2nd year interest = 330