Question

Suppose $5,400 is invested in an account at an annual interest rate of 3.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

Answer #1

For interest compounding continuously, we need this formula:

A = Pe^{rt}

A is Amount at some time t

P is the initial amount

r is the interest rate (as a decimal)

t is number of years

A = 10,800 (since we want the investment to double)

P = 5,400

r = 0.039

A = Pe^{rt}

10800=5400*e^{(0.039*t)}

2=e^{(0.039*t)}

takingnatural logarithmon both sides we get

ln(2)=(0.039*t)ln(e)

t=ln(2)/0.039

t=0.693/0.039

t=17.773 years

t=18 years(rounding to nearest tenth of a year)

**It will take 18 years for the investment to double in
size.**

Suppose $40,000 is invested in an account that returns 7% per
year compounded continuously. (Round your answers to one decimal
place.)
a. how long will it take for the investment to double? ____
yrs
b. How long will it take for the investment to triple? _____
yrs

Suppose $12,500 is invested in an account which offers 3.25%
interest compounded quarterly (4 times a year).
(a) Express the amount A in the account as a function of the
term of the investment t in years.
(b) How much would be in the account in 7 years (assuming non
deposits or withdrawals are made)?
(c) How long will it take for the initial investment to double
(round the nearest tenth of a year)?

Adam deposited $1500 in an account in which interest is
compounded continuously. The annual rate of interest is 2.5 %. How
long does it take for his money to double?

Suppose $5000 is invested at an annual interest rate of 4.15% if
compounded continuously.
a) Compute the balance at the end of 16 years.
b) What is the doubling time (round to the nearest year)?
c) What will be the balance at the end of 16 years if computed
quarterly?

An initial deposit is made of $12,000 in an account paying 4%
interest compounded continuously. a. How much will the account be
worth in 6 years? b. How long will it take the account to
double?

10. Suppose $14,000 is invested in a quarterly compounded
account at 3.58%. Approximately how long will it take for the
balance to reach $37,100?
____ year (Round the answer to the nearest tenth of a
year.)
13. If income tax varies directly with income and a person
earning $32,000 per year pays $8,320 in taxes, how much will a
person earning $46,000 per year pay?
$________

An investment of 9,000 earns interest at an annual rate of 7%
compounded continuously. Find the instantaneous rate of change of
the amount in the account after 1 year.

$2000 is deposited with an annual interest of 2% compounded
continuously.
(a) Find the balance of the account in 5 years
(b) How long will it take for the money to become 3 times at
this rate?

How much will $100 grow to if invested at a continuously
compounded interest rate of 7.5% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 7.5 years? (Do
not round intermediate calculation

How much will $100 grow to if invested at a continuously
compounded interest rate of 8.5% for 9 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 9% for 8.5 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)

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