How long does it take for an investment to double in value if it is invested at 10% compounded quarterly?

How long does it take for an investment to double in value if it is invested at 14 % compounded quarterly and compounded continuously?
a) At 14% compounded quarterly, the investment doubles in how many years?
b) At 14% compounded continuously, the investment doubles in how many years?

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Expert Answer

Step 1
Compound interest:
In compound interest, interest is added back to the principal sum so that interest is earned on that added during the next compounding period. That is, compound interest will give an interest on the interest. The interest payments will change in the time period in which the initial sum of money stays in the bank or with the barrower.
The general formula for compound interest is,
A=P⋅(1+r n)nt
Where:
A is the future value of the investment loan including the loan,
P is the principle amount,
r is the annual interest rate in decimals,
n is the number of times interest is compounded per year,
t is the time of years the money is invested or borrowed.
Step 2
a) Find the number of years in which the investment will be doubled at 14% interest compounded quarterly:
The aim is to double the invested or principal amount at the given interest rate.
The future value of the investment loan including the loan should be the double of principal amount at 14 % interest compounded quarterly.
Here,
Let the principal amount or the invested amount is P.
The future value of the invested amount including the amount is A= 2P
Annual interest rate is r=14% =0.14
The number of times interest is compounded per year is quarterly. That is, n=4.
The number of years required to double the invested money is invested t.
The number of years in which the investment will be doubled at 14% interest compounded quarterly is obtained as 5.04 years from the calculation given below:
A=P×(1+rn)nt
2P=P×(1+0.144)4t
2=(1+0.035)4t
2=(1.035)4t
Take natural logaritm on both sides
ln⁡(2)=ln⁡(1.0354t)
=4 tln⁡(1.035)
t=ln⁡(2 )4×ln⁡(1.035)
=5.04
Step 3 Continuous compound interest:
In compound interest, interest is added back to the principal sum so that interest is earned on that added during the next compounding period. That is, compound interest will give an interest on the interest.
In continuous compound interest, the principal amount will be constantly earning interest and the interest keeps earning on the interest earned.
The general formula for continuous compound interest is,
A=P⋅ ert
Where:
A is the future value of the investment loan including the loan,
P is the principle amount,
r is the interest rate in decimals,
t is the time of years the money is invested or borrowed.
Step 4
b) Find the number of years in which the investment will be doubled at 14% interest compounded continuously:
The aim is to double the invested or principal amount at the given interest rate.
The future value of the investment loan including the loan should be the double of principal amount at 14% interest compounded continuously.
Here,
Let the principal amount or the invested amount is P.
The future value of the invested amount including the amount is A=2P
Annual interest rate is r=14%=0.14,
The number of years required to double the invested money is invested t.
The number of years in which the investment will be doubled at 14% interest compounded continuously is obtained as 4.95 years from the calculation given below:
A =P× ert
2P=P× ert
2=ert
Take natural logarithm on both sides
ln⁡(2)=ln⁡(e rt)
ln⁡ (2)=rt
t=ln⁡(2) r
=ln⁡(2)0.14; [ ∵ r=14%=0.14]
=4.95
Step 5
Answer: a) In 5.04 years, the investment will be doubled at 14% interest compounded quarterly.
b) In 4.95 years, the investment will be doubled at 14% interest compounded continuously.

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• How long will it take money to double if it is invested at 10% compounded continuously?
• How long will it take for an investment to double if it is invested at 10% simple interest?
• How long would it take for an investor to double his money at 10% interest per year compounded annually?
• How long does it take for an investment to double in value if it is invested at 4 compounded quarterly?

How long will it take money to double if it is invested at 10% compounded continuously?

A 10% interest rate will double your investment in about 7 years (72 ∕ 10 = 7.2); an amount invested at a 12% interest rate will double in about 6 years (72 ∕ 12 = 6). Using the Rule of 72, you can easily determine how long it will take to double your money.

How long will it take for an investment to double if it is invested at 10% simple interest?

How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double ((1.107.3 = 2).

How long would it take for an investor to double his money at 10% interest per year compounded annually?

Given a 10% annual rate of return, how long will it take for your money to double? Take 72 and divide it by 10 and you get 7.2. This means, at a 10% fixed annual rate of return, your money doubles every 7 years.

How long does it take for an investment to double in value if it is invested at 4 compounded quarterly?

If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.

How long will it take for an investment to double if it is invested at 10% simple interest?

How many years would it take your money to double A at 10% 10 interest compounded yearly?

How long does it take for an investment to double in value if it is invested at 10% compounded monthly compounded continuously?

How long will it take to double your money at 10% per year?