Answer:
1.) The balance is of $22,330.86
2.) Gain of $2,330.86
3.) Less of a gain.
Explanation:
Initially, we have $20.000.
We make the following investments:
All of them for 3 years.
45%, with interest 4.35% at a treasure bond.
15%, with interest 3.75%, at the CD.
20% in the stock. Increases 8%, then decreases 4%, then increases 6%.
Remainder(100 - (45+15+20)) = 20% in savings, with 2.9% interest.
1. Balance at the end of the third year:
How much money you will have, this is the sum of the four investments.
Treasure bond:
0.45*20000 = 9000.
9000 invested in treasure bond. In 3 years you will have.
4.35% = 0.0435
Tr = 9000*(1 + 0.0435)^3 = 10226.33
CD:
0.15*20000 = 3000
Cd = 3000*(1 + 0.0375)^3 = 3350.31
Stock:
0.2*20000 = 4000
Increases 8%(multiplies by 1 + (8/100) = 1.08), decreases by 4%(multiplies by 1 - (4/100) = 0.96), increases by 6%(multiplies by 1 + (6/100) = 1.06). So
St = 4000*1.08*0.96*1.06 = 4396.03
Savings:
0.2*20000 = 4000
Sa = 4000*(1 + 0.029)^3 = 4358.19
Balance:
The sum.
B = Tr + Cd + St + Sa = 10226.33 + 3350.31 + 4396.03 + 4358.19 = 22330.86
2.
You invested $20000.
Now you have $22330.86.
So you earned 22330.86 - 20000 = 2330.86.
So a gain of $2,330.86
3.
In the first exercise, we found a balance of 22330.86.
Now we have to find the Balance if we had invested 45% in stock and 20% in treasure, that is, if we had switched those two applications. So
Treasure bond:
0.2*20000 = 4000.
4000 invested in treasure bond. In 3 years you will have.
4.35% = 0.0435
Tr = 4000*(1 + 0.0435)^3 = 4545.04
CD:
0.15*20000 = 3000
Cd = 3000*(1 + 0.0375)^3 = 3350.31
Stock:
0.452*20000 = 9000
Increases 8%(multiplies by 1 + (8/100) = 1.08), decreases by 4%(multiplies by 1 - (4/100) = 0.96), increases by 6%(multiplies by 1 + (6/100) = 1.06). So
St = 9000*1.08*0.96*1.06 = 9891.07
Savings:
0.2*20000 = 4000
Sa = 4000*(1 + 0.029)^3 = 4358.19
Balance: 4545.04 + 3350.31 + 9891.07 + 4358.19 = 22144.61
The balance is smaller than in the first case, so you would have less of a gain.