Question

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?

Answer #1

The time needed to double the deposited amount of $1500 to $3000 is calculated with the following equation

FV= P*e^rt

Where, FV is the future value of the investment

P is the initial principal amount

r rate of interest

t is time period

3000 = 1500*e^0.025t

e^0.025t = 3000/1500

lne^0.025t = ln2 (taking natural natural log on both sides)

Since lnex =x

0.025t = ln2

t =ln2/0.025

t = 0.693147/0.025

t = 27.73

Therefore, it will take 27.73 years for the investment to double.

$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?

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:

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?

Find the nominal annual rate of interest
a) at which $1500 will grow to $1800 in four years compounded
compounded monthly
b) at which money will double in seven years if compounded
quarterly

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 8 years when
$5000 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...

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 8 years when
$5000 is deposited in a savings account drawing 5 3/4
% annual interest compounded continuously. (Round your answer to
the nearest cent.)
$
(b) this is the part I’m having the...

1. If you deposit $6,500 into an account paying 8% annual
interest compounded monthly, how much money will be in the account
after 7 years?
2. If you deposit $5,000 into an account paying 6% annual
interest compounded monthly, how long until there is $8,000 in the
account?
3. At 3% annual interest compounded monthly, how long will it
take to double your money?

3. Matt invested $5,500 into an account earning 2.5% APR
compounded continuously. What will his balance be after seven
years?
4. How much money should be deposited in an account today that
earns 3.5% compounded monthly so that it will accumulate to $10,000
in 8 years?

Money is continuously deposited into an account at a rate of $M
per year.

7. What is the effective annual interest rate for a bank account
that pays a continuously compounded interest rate of 8%?

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