You saved $20,000.00 and want to diversify your monies. You invest 45% in a Trea

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? Be sure to include in your response: · Detailed calculations for each type of investment. · Answers to the original questions.

Explanation / Answer

1.

here

we use the formula

FV = PV (1+i)n

PV = Present Value
FV = Future Value
i = Discount rate
n = Number of periods

here we are having different APR and different % of investment so we caluculate each one individually using the above formula and then add them to get the final.

PV = $20,000 is common value in all cases

now

take APR = 4.35%

investtment =45%

FV = 20000 x 45% x (1 + 4.35%)3 = 10,226.33

now

take APR =3.75%

investtment =15%

FV = 20000 x 15% x (1 + 3.75%)3 =3,321.33

now

take APR =

8 % increase so +

4% decrease so -

6% increase so +

investtment =20%

FV = 20000 x 20% x (1 + 8%) x (1 - 4%) x (1 + 6%) = 4,396.03

now

take APR =2.90%

investtment =20%

FV = 20000 x 20% x (1 + 2.90%)3 = 4,358.18

Total value = 10,226.33 +3,321.33 +4,396.03 +4358.18 =$22,301.87

2.

Gain = $22,301.87 - 20,000 = $2301.87

3.

If you had invested 45% in stock and 20% in Treasury bonds

then

take APR = 4.35%

investtment =20%

FV = 20000 x 20% x (1 + 4.35%)3 = 4545.03

now

take APR =3.75%

investtment =15%

FV = 20000 x 15% x (1 + 3.75%)3 =3,321.33

now

take APR =

8 % increase so +

4% decrease so -

6% increase so +

investtment =20%

FV = 20000 x 20% x (1 + 8%) x (1 - 4%) x (1 + 6%) = 4,396.03

now

take APR =2.90%

investtment =45%

FV = 20000 x 45% x (1 + 2.90%)3 = 9805.92

Total value = 4545.03 +3,321.33 +4,396.03 +9805.92 =$22068.31

now

$22068.31- 20,000 = $2068.31

we will have $2301.87 - $2068.31 = $233.56 less gain

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