Question

Since 2007, a particular fund returned 13.8% compounded monthly. How much would a $6000 investment in this fund have been worth after 2 years? (Round your answer to the nearest cent.)

Answer 1

Answer 2

Answer:

Future Value ≈ $7,821.43

Steps:

1. Given:

• Principal ($P$) = $6,000

• Annual rate ($r$) = 13.8% = 0.138

• Compounding frequency ($n$) = 12 (monthly)

• Time ($t$) = 2 years

2. Formula (Compound Interest):

   $$A=P{(1+\frac{r}{n})}^{nt}$$

3. Calculate:

   $$A=6000{(1+\frac{0.138}{12})}^{12\times 2}=6000{\left(1.0115\right)}^{24}\approx 6000\times 1.30357\approx 7,821.43$$

Final Amount: $7,821.43 (Rounded to nearest cent).

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Key Notes:

• Monthly rate = $\frac{13.8\mathrm{\%}}{12}=1.15\mathrm{\%}$.

• Total compounding periods = $2\times 12=24$.

• Used $1.0115^{24}\approx 1.30357$ via calculator.