Answer :
Answer:
1. 10,000 in treasury, 8750 in CD and 6250 in stock
2. 11329.96 in treasury bonds, 9603.20 in CD and 6868.8 in stocks
3. 2801.96in profit
4. You would have mad more money in stocks because it grew the most
Step-by-step explanation:
25,000x0.40=10000 in treasury
25000x0.35=8750 in CD
25000x0.25 =6250 stock
10000(1+0.0425)^3= about 11329.96 treasury bonds
8750(1+0.0315)^3=about 9603.20 in CD
6250x1.08 (1st year) =6750
6750x0.96=6480 (second year)
6480x1.06=6868.8 (third year) 6868.8 in stocks
11329.96+9603.20+6868.8=27801.96 total balance
2801.96 profit
Answer:
1) Treasury bond = $10,000
CD = $8,750
Stock = $6,250
2) Treasury bond = $11,329.96
CD = $9,603.20
Stock = $6,868.80
3) Gain = $2,801.96
4) Less of a gain ($2,674.50)
Step-by-step explanation:
Question 1
Given:
- Total investment = $25,000.00
Allocation:
- Treasury bond = 40%
- CD = 35%
- Stock = 25%
To calculate the initial investment for each account, multiply the total investment by the corresponding percentage:
[tex]\textsf{Treasury bond}=\$25000 \times 40\%=\$10000\\\\\textsf{CD}=\$25000 \times 35\%=\$8750\\\\\textsf{Stock}=\$25000 \times 25\%=\$6250[/tex]
[tex]\dotfill[/tex]
Question 2
To determine the balance for each investment type at the end of the third year, we can use the compound interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
Treasury bond:
- P = $10,000
- r = 4.25% = 0.0425
- n = 1 (annually)
- t = 3 years
Therefore:
[tex]\textsf{Treasury bond balance}=10000\left(1+\dfrac{0.0425}{1}\right)^{1 \cdot 3}\\\\\\\textsf{Treasury bond balance}=10000\left(1.0425\right)^{3}\\\\\\\textsf{Treasury bond balance}=11329.96[/tex]
So, there will be $11,329.96 in the Treasury bond account at the end of the third year.
CD account:
- P = $8,750
- r = 3.15% = 0.0315
- n = 1 (annually)
- t = 3 years
Therefore:
[tex]\textsf{CD balance}=8750\left(1+\dfrac{0.0315}{1}\right)^{1 \cdot 3}\\\\\\\textsf{CD balance}=8750\left(1.0315\right)^{3}\\\\\\\textsf{CD balance}=9603.20[/tex]
So, there will be $9,603.20 in the CD account at the end of the third year.
The stock plan is more complicated as it increases by 8% the first year, decreases in value by 4% the second year, and increases by 6% the third year. Therefore, we need to calculate the value at the end of each year and compound accordingly.
[tex]\textsf{Stock balance (end of year 1)}=6250\left(1+0.08\right)\\\\\textsf{Stock balance (end of year 1)}=6250\left(1.08\right)\\\\\textsf{Stock balance (end of year 1)}=6750[/tex]
[tex]\textsf{Stock balance (end of year 2)}=6750\left(1-0.04\right)\\\\\textsf{Stock balance (end of year 2)}=6750\left(0.96\right)\\\\\textsf{Stock balance (end of year 2)}=6480[/tex]
[tex]\textsf{Stock balance (end of year 3)}=6480\left(1+0.06\right)\\\\\textsf{Stock balance (end of year 3)}=6480\left(1.06\right)\\\\\textsf{Stock balance (end of year 3)}=6868.80[/tex]
So, there will be $6,868.80 in the stock account at the end of the third year.
[tex]\dotfill[/tex]
Question 3
To find the total gain, we sum up the balances of all three accounts at the end of the third year and then subtract the initial investment of $25,000.
[tex]\textsf{Total gain}=11329.96+9603.20+6868.80-25000\\\\\textsf{Total gain}=2801.96[/tex]
Therefore, the total gain from all the investments combined is $2,801.96.
[tex]\dotfill[/tex]
Question 4
To determine if we would have more or less of a gain after the three years if we had invested 25% in treasury bonds and 40% in stock, we need to repeat the calculations we performed in question 2, but with the new allocations.
Treasury bond:
- P = 25% of $25,000 = $6,250
- r = 4.25% = 0.0425
- n = 1 (annually)
- t = 3 years
Therefore:
[tex]\textsf{Treasury bond balance}=6250\left(1+\dfrac{0.0425}{1}\right)^{1 \cdot 3}\\\\\\\textsf{Treasury bond balance}=6250\left(1.0425\right)^{3}\\\\\\\textsf{Treasury bond balance}=7081.22[/tex]
So, there will be $7,081.22 in the Treasury bond account at the end of the third year.
Stock:
- P = 40% of $25,000 = $10,000
- r = 8%, -4%, 6%
Therefore:
[tex]\textsf{Stock balance (end of year 1)}=10000\left(1+0.08\right)\\\\\textsf{Stock balance (end of year 1)}=10000\left(1.08\right)\\\\\textsf{Stock balance (end of year 1)}=10800[/tex]
[tex]\textsf{Stock balance (end of year 2)}=10800\left(1-0.04\right)\\\\\textsf{Stock balance (end of year 2)}=10800\left(0.96\right)\\\\\textsf{Stock balance (end of year 2)}=10368[/tex]
[tex]\textsf{Stock balance (end of year 3)}=10368\left(1+0.06\right)\\\\\textsf{Stock balance (end of year 3)}=10368\left(1.06\right)\\\\\textsf{Stock balance (end of year 3)}=10990.08[/tex]
So, there will be $10,990.08 in the stock account at the end of the third year.
Sum up the two new account balances with the previously calculated CD balance:
[tex]7081.22+10990.08+9603.20=27674.50[/tex]
Now, subtract the initial investment of $25,000 to calculate the new gain:
[tex]\textsf{New gain}=27674.50-25000\\\\\textsf{New gain}=2674.50[/tex]
As $2,674,50 is less than $2,801.96, we would have less of a gain after the three years if 25% was invested in treasury bonds and 40% was invested in stock.
