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. You invest 20% 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.What are the balances for each type of investment at the end of the third year?

Answer 1

Compound Interest

A total of $20,000 is invested in different assets.

45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.

For this investment, the principal is P = 0.45*$20,000 = $9,000.

The compounding period is yearly, thus the interest rate is:

i = 4.35 / 100 = 0.0435

The duration (in periods) is n = 3

Calculate the final value with the formula:

$M=P_{}(1+i)^n$

Substituting:

$\begin{gathered} M=\ 9,000_{}(1+0.0435)^3 \\ M=\ 9,000\cdot1.136259062875 \\ M=\ 10,226.33 \end{gathered}$

The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:

P = 15% of $20,000 = $3,000

i = 3.75 / 100 = 0.0375

n = 3

Calculating:

$\begin{gathered} M=\ 3,000_{}(1+0.0375)^3 \\ M=\ 3,000\cdot1.116771484375 \\ M=\ 3,350.31 \end{gathered}$

The third investment is in a stock plan. The initial value of the investment is

P = 20% of $20,000 = $4,000

By the end of the first year, the stock plan increased by 8%, thus its value is:

M1 = $4000 * 1.2 = $4,800

By the end of the second year, the stock plan decreased by 4$, thus the value is:

M2 = $4,800 * 0.96 = $4,608

Finally, the stock plan increases by 6%, resulting in a final balance of:

M3 = $4,608 * 1.06 = $4,884.48

Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).

P = $20,000 - $9,000- $3,000 - $4,000 = $4,000

i = 2.90 / 100 = 0.029

n = 3

Calculating:

$\begin{gathered} M=\ 4,000_{}(1+0.029)^3 \\ M=\ 4,000\cdot1.089547389 \\ M=\ 4,358.19 \end{gathered}$

To summarize, the final balances for each type of investment at the end of the third year are:

Investment 1; $10,226.33

Investment 2: $3,350.31

Investment 3: $4,884.48

Investment 4: $4,358.19

Total balance: $22,819.32