Pathology studies the<br> a<br> and effect of disease.

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t

liubo4ka [24]

Answer:

a) - r=5%: $S=$ 5,136.10$

- r=4%: $S=$ 4,885.61$

- r=3%: $S=$ 4,647.34$

b) - r=5%: t=14 years

- r=4%: t=17 years [/tex]

- r=3%: t=23 years [/tex]

c) The amount obtained is

- Compuonded quarterly: $5,191.83

- Compuonded continously: $5,200.71

The latter is always greater, since the more often it is capitalized, the greater the effect of compound interest and the greater the capital that ends up accumulating.

Explanation:

The rate of accumulation of money is

$dS/dt=rS$

To calculate the amount of money accumulted in a period, we have to rearrange and integrate:

$\int dS/S=\int rdt=r \int dt\\\\ln(S)=C*r*t\\\\S=C*e^{rt}$

When t=0, S=S₀ (the initial capital).

$S=S_0=Ce^{r*0}=Ce^0=C\\\\C=S_0$

Now we have the equation for the capital in function of time:

$S=S_0e^{rt}$

a) For an initial capital of $4000 and for a period of five years, the amount of capital accumulated for this interest rates is:

- r=5%: $S=4000e^{0.05*5}=4000*e^{0.25}= 5,136.10$

- r=4%: $S=4000e^{0.04*5}=4000*e^{0.20}= 4,885.61$

- r=3%: $S=4000e^{0.03*5}=4000*e^{0.15}= 4,647.34$

b) We can express this as

$S=S_0e^{rt}\\\\2S_0=S_0e^{rt}\\\\2=e^{rt}\\\\ln(2)=rt\\\\t=ln(2)/r$

- r=5%: $t=ln(2)/0.05=14$

- r=4%: $t=ln(2)/0.04=17$

- r=3%: $t=ln(2)/0.03= 23$

c) When the interest is compuonded quarterly, the anual period is divided by 4. In 5 years, there are 4*5=20 periods of capitalization. The annual rate r=0.0525 to calculate the interest is also divided by 4:

$S = 4000 (1+(1/4)(0.0525))^{5*4}=4000(1.013125)^{20}\\\\S=4000*1.297958= 5,191.83$

If compuonded continously, we have:

$S=S_0e^{rt}=4000*e^{0.0525*5}=4000*1.3= 5,200.71$

The amount obtained is

- Compuonded quarterly: $5,191.83

- Compuonded continously: $5,200.71

The latter is always greater, since the more often it is capitalized, the greater the effect of compound interest and the greater the capital that ends up accumulating.

5 0

4 years ago

Bill's tendency to consider evidence that supports his position on illegal immigration, but disregards evidence that refutes his

Anit [1.1K]

an example of overconfidence would be: Joe makes a stock price prediction and believes that there is only a 5% chance that his estimate is wrong; overlooking recent articles about the bad financial health of the business.

Buying stocks without any prior knowledge in finance would provide people with 50% rate of success. Good stock traders usually could improve their success rate up to 70% while success rate of 95% is very unlikely. Especially if the financial information showed a bad sign. The fact that Bill still put his money on the company's stock indicates that he is overconfident.

4 0

4 years ago

nformation concerning Johnston Co.'s direct materials costs is as follows: Standard price per pound $ 6.45 Actual quantity purch

Dmitry [639]

Answer:

f. $615

Explanation:

The standard cost for 2,850 pounds is $18,328.5 (=$6.45 * 2,850)

Materials purchase-price variance–favourable $855; it means standard price is higher and actual material price. Then we have actual cost for purchased 2,850 pounds is $17,527.5 (=$18,328.5-$855)

Then the actual price per pound $6.15 (=$17,527.5/2,850)

The difference between purchased and actual quantity used is 100 pounds (= 2,850 pounds - 2,750 pounds)

The direct materials usage variance for the period is $650 (= $6.15 * 100 pounds)

4 0

3 years ago

Foster Gardening manufactures and sells garden supplies. Last month, Foster had a controllable margin of $1.6 million, which was

Tanya [424]

budget variance was the difference in ROI between the budgeted and actual amounts

<h3>What is budget variance?</h3>

A budget variance is an accounting term that refers to situations in which actual costs are higher or lower than the standard or projected costs. An unfavorable, or negative, budget variance indicates a budget shortfall, which can occur when revenues fall short or costs exceed expectations.

Typically, variance reports are used to examine the gap between budgeted and actual performance. Depending on the financial outcomes being compared, the variance report may also be referred to as "budget variance" or simply "variance." The difference between the budgeted/baseline goal and the actual reality is referred to as "variance."

Budget variance equals the difference between the budgeted amount of expense or revenue, and the actual cost.

To know more about budget variance follow the link:

brainly.com/question/25790358

#SPJ4

4 0

2 years ago

Which of the following statements is TRUE?A. As the probability of a super-event decreases, the advantage of utilizing multipl

scZoUnD [109]

Answer:

D

Explanation:

Studying MGMT 4010 Ch S11 on Quizlet: https://quizlet.com/304737596/mgmt-4010-ch-s11-flash-cards/?x=1jqU&i=utx3h

8 0

4 years ago

Pathology studies the a and effect of disease.