Question

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

Answer #1

Given; principal=$40,000, rate=7%

a)amount=$80,000, b) $120,000

we have to find time.

Formula for calculation of compound intrest

**A=P(1+r/n)n*t** where

a). A= amount + $80,000

P=principal =$40,000

r= intrest rate in decimal=0.07

n= number of times intrest is componded per unit time= 1

t= time in years

put all these values in above formula

$80,000=$40,000(1+0.07)t

2=1.07t

take ln on both side

ln(2)=t ln(1.07)

**t=ln(2)/ln(1.07)= 10.25 years.**

**B)** amount=$120,000

$120,000=$40,000(1+0.07)t

3=(1+0.07)t

take ln on both side

ln(3)=ln(1.07)*t

**t=ln(3)/ln(1.07)=16.237 years**

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:

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)?

You invest $3500 in an account at interest rate r,
compounded continuously. Find the time required for the amount to
double and triple. (Round your answers to two decimal places.)

1)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. How much is our account worth
after 7 years? Round your answer to the nearest penny.
2)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. If we make these deposits for 7
years, what is the present value of this account? Round your answer
to the nearest penny.

How long (in years) would $500 have to be invested at 7%,
compounded continuously, to amount to $905? (Round your answer to
the nearest whole number.)

If $9,000 is invested at 9% per year compounded monthly, the
future value S at any time t (in months) is given
by S = 9,000(1.0075)t.
(a) What is the amount after 1 year? (Round your answer to two
decimal places.)
$
(b) How long before the investment doubles? (Round your answer to
one decimal place.)
months

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 12% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 12 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =

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?
$________

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