Hot answers tagged finance
2
Price $P$. Residual value, or the amount for which you can successfully sell the car after $L$ months, $R$. Hence amount you are actually borrowing is effectively $B=P-R$.
Now you are paying a total of $T = L\times M$ where $M$ is the monthly payment. Therefore the percentage difference in the amount you pay versus the amount you borrow is
$$I=100\%\times( ...
1
When one does mathematics, it can be useful to go back to basic principles.
With interest rate of $0.07$, that is, $7\%$, compounded annually, in $n$ years $A$ dollars grow to
$$A(1.07)^n$$
dollars. In our case, $1500$ grew to $3750$ in an unknown number $n$ of years, so
$$3750=1500(1.07)^n.$$
It follows that
$$(1.07)^n=\frac{3750}{1500}=2.5.$$
Take the ...
1
This is good, subject to revising your typo. You have after $n$ periods that your balance is
$$1500* 1.07^n.$$
Now set $$1500*1.07^n = 3750.$$
Begin by dividing to get
$$1.07^n = 2.5 $$
so
$$n = {\log(2.5)\over \log(1.07)} = 13.54.$$
Your answer is off a bit because you transposed two digits.
1
If by chance you didn't want to use logarithm's you could make a table and write the formula out for the desired years:
$a(1+r)^n$
where $a$ is the initial amount, $r$ is the rate and $n$ is the number of years.
For year 12: $1500(1+0.07)^{12}$ = 3378.29
For year 13: $1500(1+0.07)^{13}$ = 3614.77
For year 14: $1500(1+0.07)^{14}$ = 3867.29
So if the ...
1
Here is an answer done "their" way-
We have $$1300=500(1.06)^n$$ $$\implies 13=5(1.06)^n$$ $$\implies \frac{13}{5}=(1.06)^n$$ $$\implies \log_{1.06}\frac{13}5 =n$$ $$\implies n \approx 16.39830702$$ $$\implies n \approx 16.4$$ Rounded to one decimal place.
Please ask if you need any further clarification.
1
The 1.102 comes from two places.
First, "%" means hundredths. If you see "10.2%", that really means $\frac{10.2}{100}$, which is 0.102.
Second, if your money is earning 10.2% interest annually, that means that at the end of the year, the bank takes your balance, multiplies it by 10.2%—that is, by 0.102—and hands you that much more in interest.
Your new ...
1
To get a solution, you'll need to specify an objective that you are trying to maximize.
If you are just maximizing the expected profit, then your \$15,000 answer is correct.
Typically, however, in finance we assume people are risk-averse. A standard objective function in that case is $E[profit] - \lambda * Var[profit]$ where $\lambda$ is the level of ...
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