# 3. Compute the nominal annual rate of interest compounded semi-annually on a loan of $48000 repaid in

###### Question:

## Answers

Rate = 51.74%

Step-by-step explanation:

Principal amount= $48000

Amount paid is done 2 times in a year for ten years

= $4000*2*10

Amount paid= $80000

A= p(1+r/n)^nt

80000= 48000(1+r/20)^(20*10)

(80000/48000)= (1+r/20)^(200)

(200)√(1.6667)= 1+ r/20

1.025870255-1= r/20

0.025870255*20= r

0.5174= r

Rate in decimal= 0.5174

In percentage= 51.74%

1.$3,187.69 Rounded= $3,187.70

2. $8,456.03

3. $39,846.20

4. Is that the whole problem?

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4000\\ r=rate\to 2\%\to \frac{2}{100}\to &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.02}{1}\right)^{1\cdot 4}\implies A=4000(1.02)^4\implies A\approx 4329.73[/tex]

then she turns around and grabs those 4329.73 and put them in an account getting 8% APR I assume, so is annual compounding, for 7 years.

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4329.73\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &7 \end{cases} \\\\\\ A=4329.73\left(1+\frac{0.08}{1}\right)^{1\cdot 7}\implies A=4329.73(1.08)^7\\\\\\ A\approx 7420.396[/tex]

add both amounts, and that's her investment for the 11 years.

a. $4,415.25

b. $4,376.70

c. 2.27986 years

Step-by-step explanation:

a.

A = 4,000 (1 + 0.05/2)^(2 x 2)

= $4,415.25

b.

A = 4,000 x e^(0.045 x 2)

= $4,376.70

c. $100 more than option 2 = 4,376.70 + 100

= $4,476.70

t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)

= 2.27986 years

For the first question water and electric bill since they are bills that you have to pay

Second Question is 846,285 since I think you add them together And I can't answer the last to parts