When interest is compounded continuously, the amount of money increases at a rate proportional to the amount s present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) find the amount of money accrued at the end of 5 years when $4000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (round your answer to the nearest cent.) $ (b) in how many years will the initial sum deposited have doubled? (round your answer to the nearest year.) years (c) use a calculator to compare the amount obtained in part (a) with the amount s = 4000 1 + 1 4 (0.0575) 5(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.) s = $

a) - r=5%:

- r=4%:

- r=3%:

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

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

When t=0, S=S₀ (the initial capital).

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

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%:

- r=4%:

- r=3%:

b) We can express this as

- r=5%:

- r=4%:

- r=3%:

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:

If compuonded continously, we have:

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.

you had 23.00$ because 28 - 5 = 23 then put it in dollar form

d. the economy will face inflation.