Question

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 $6000 is deposited in a savings account drawing 534% 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.)
c) Use a calculator to compare the amount obtained in part a) with the amount S=6000(1+14(0.0575))5(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)

Answer 1

See explanation

Step-by-step explanation:

Given that;

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

Where;

P= $6000

r = 5 3/4%

t = 5 years

n= 1

A = 6000(1 + 0.0575)^5

A= $ 7935

b) What time will A become $12,000

12000 = 6000(1 + 0.0575)^t

12000/6000 = (1 + 0.0575)^t

2 = (1 + 0.0575)^t

Take logarithm of both sides

log2 = t log(1 + 0.0575)

t= log2/log(1 + 0.0575)

t= 0.3010/0.0243

t = 12 years

c) when compounded quarterly;

S= 6000(1 + 1/4(0.0575))^(5)(4)

S= $7982

The amount when interest is compounded quarterly is higher than when it is compounded annually because the interest increases as the number of compounding periods increases.