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There are many online student loan calculators that can assist you. Examine the input boxes for one such calculator (Cost of Interest Capitalization Calculator

 Loan Balance 5500 Interest Rate 4.29 Deferment in Months 54 Capitalization  At Repayment  Loan Term in Years 10\begin{array}{lc} \text { Loan Balance } & 5500 \\ \text { Interest Rate } & 4.29 \\ \text { Deferment in Months } & 54 \\ \text { Capitalization } & \text { At Repayment } \\ \text { Loan Term in Years } & 10 \end{array}

After clicking "calculate" the following information is reported: Comment 1: After the deferment period of 54 months, the new loan balance is $6,561.78, including$1,061.78 in accrued interest. Comment 2: Without the interest capitalization there would have been 120 payments of $56.45 adding up to$6,774.00 (including a total of $1,274.00 in interest) plus an additional$1,061.78 in interest paid during the deferment period. Comment 3: With the interest capitalization, there are 120 payments of $67.34 for a total payment of$8,080.80 (including a total of $1,519.03 in interest plus$1,061.78 in interest accrued during the deferment period). Comment 4: The total amount paid with interest capitalization is $8,080.80, or$245.03 more than would have been paid without capitalization. That's an extra $0.04 for every dollar borrowed. Answer the questions below based on the comments above. Examine comment 3. Explain the way in which a student chose to make payments if this comment applies.


This exercise concerns a single investment of $10,000. Find the continuous interest rate per year, yielding a future value of$20,000 in the given time period. 5 years


Answered three weeks ago
Answered three weeks ago
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1 of 2

Consider Present value is 10,00010,000 and future value is 20,00020,000 in 15 years then the future value is

B=PertB=P e^{rt}

Here BB is future value and PP is present Value

Consider a single deposit of $10000\$10000 and future value of $20000\$20000 in 60 year time period.

20000=10000er(5)2=er(5)\begin{align*} 20000 &=10000 e^{r(5)} \\ 2 &=e^{r(5)} \end{align*}

ln2=lner(s)ln2=r×5ln25=rr=0.1386\begin{align*} \ln 2 &=\ln e^{r(s)} \\ \ln 2 &=r \times 5 \\ \frac{\ln 2}{5} &=r \\ r &=0.1386 \end{align*}

r=0.1386×100=13.86%\begin{align*} r &=0.1386 \times 100 \\ &=13.86 \% \end{align*}

Thus the interest rate 13.86%13.86 \% which yields a future value of 20,00020,000 in time period of 5 years

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