Respuesta :
Answer:
(a) 6.2% compounded annually: $5474.78
(b) 6.2% compounded semiannually: $5524.52
(c) 6.2% compounded quarterly: $5550.32
Explanation:
For an investment at compound interest, the value of the investment at the end of t years is calculated using the formula:
[tex]A(t)=P\left(1+\frac{r}{k}\right)^{tk}\text{ where }\begin{cases}P=\text{Principal Invested} \\ r=\text{Interest Rate} \\ k=\text{Number of compounding periods}\end{cases}[/tex]Given:
• Principal Amount = $3,000
,• Time = 10 years
(a)6.2% compounded annually
• Rate = 6.2% = 0.062
,• k=1 (Annually)
[tex]\begin{gathered} A(10)=3000\left(1+\frac{0.062}{1}\right)^{10\times1} \\ A(10)=\$5474.78 \end{gathered}[/tex]If the interest rate is 6.2% compounded annually, the value of the investment at the end of 10 years is $5474.78.
(b)6.2% compounded semiannually
• Rate = 6.2% = 0.062
,• k=2 (semiannually)
[tex]\begin{gathered} A(10)=3000\left(1+\frac{0.062}{2}\right)^{10\times2} \\ A(10)=\$5524.52 \end{gathered}[/tex]If the interest rate is 6.2% compounded semiannually, the value of the investment at the end of 10 years is $5524.52
Part C: 6.2% compounded quarterly
• Rate = 6.2% = 0.062
,• k=4 (quarterly)
[tex]\begin{gathered} A(10)=3000\left(1+\frac{0.062}{4}\right)^{10\times4} \\ A(10)=\$5550.32 \end{gathered}[/tex]If the interest rate is 6.2% compounded quarterly, the value of the investment at the end of 10 years is $5,550.32
Part D: 6.2% compounded monthly
