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 $5000 is invested in an account at an annual interest
rate of 6.8% compounded continuously. How long (to the nearest
tenth of a year) will it take the investment to double in size?

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 Iām having the...

Greg deposited $700 in his new savings account with the annual
interest rate of 8% on April 1, 2019
(A) The interest for this savings account is compounded once
every two months. Find the balance on this account on October 1,
2023 rounded to the nearest cent.
(B) With the assumptions in (A), how many years does it take for
the initial investment to triple? round to one decimal place

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?

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