You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded annually. You place 15% in a CD at 3.75% APR for 3 years compounded annually. 20% you invest in a stock plan and the remainder is in a savings account at 2.90% APR compounded annually. The stock plan increases 8% the first year, decreases in value by 4% the second year, and increases by 6% the third year.

Question

You saved $20,000.00 and want to diversify your monies.  You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded annually.  You place 15% in a CD at 3.75% APR for 3 years compounded annually.  20% you invest in a stock plan and the remainder is in a savings account at 2.90% APR compounded annually.  The stock plan increases 8% the first year, decreases in value by 4% the second year, and increases by 6% the third year.

1.	What are the balances for each type of investment at the end of the third year?
2.	What is your total gain from all of the investments combined?
3.	If you had invested 45% in stock and 20% in Treasury bonds, would you have more or less of a gain after the three years?

GPT 3.5 · Answer

1. Calculating the balances for each type of investment at the end of the third year:

Treasury bond:
Principal = $20,000 * 0.45 = $9,000
Interest rate = 4.35%
Compound frequency = Annually
Time = 3 years

Future value = $9,000 * (1 + 0.0435)^3 = $9,000 * 1.142651 = $10,283.86

CD:
Principal = $20,000 * 0.15 = $3,000
Interest rate = 3.75%
Compound frequency = Annually
Time = 3 years

Future value = $3,000 * (1 + 0.0375)^3 = $3,000 * 1.11646094 = $3,349.38

Stock plan:
Principal = $20,000 * 0.2 = $4,000
Year 1: 8% increase -> $4,000 * 1.08 = $4,320
Year 2: 4% decrease -> $4,320 * 0.96 = $4,147.20
Year 3: 6% increase -> $4,147.20 * 1.06 = $4,402.67

Savings account:
Principal = $20,000 * 0.2 = $4,000
Interest rate = 2.90%
Compound frequency = Annually
Time = 3 years

Future value = $4,000 * (1 + 0.029)^3 = $4,000 * 1.088747 = $4,354.99

2. Calculating the total gain from all investments combined:

Total gain = ($10,283.86 + $3,349.38 + $4,402.67 + $4,354.99) - $20,000 = $22,391.9 - $20,000 = $2,391.90

3. If you had invested 45% in stock and 20% in Treasury bonds instead:

Treasury bond:
Principal = $20,000 * 0.20 = $4,000
Interest rate = 4.35%
Compound frequency = Annually
Time = 3 years

Future value = $4,000 * (1 + 0.0435)^3 = $4,000 * 1.142651 = $4,570.60

Stock plan:
Principal = $20,000 * 0.45 = $9,000
Year 1: 8% increase -> $9,000 * 1.08 = $9,720
Year 2: 4% decrease -> $9,720 * 0.96 = $9,331.20
Year 3: 6% increase -> $9,331.20 * 1.06 = $9,909.35

Total gain with this allocation = ($9,570.60 + $9,909.35 + $4,402.67 + $4,354.99) - $20,000 = $28,237.6 - $20,000 = $8,237.6

Therefore, you would have more of a gain after three years if you had invested 45% in stock and 20% in Treasury bonds (more than double the gain compared to the original allocation).