Calculate the length of time for #800000 to earn # 15000 if invested at 10% per annum
I don't get this question or formula because I tried it so many times but failed please help me to solve
To calculate the length of time it takes for an investment to reach a certain amount, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is #800000, the future value (A) is #15000, and the annual interest rate (r) is 10% (or 0.1 as a decimal). We need to determine the time (t) it takes for the investment to reach the future value.
Let's use an assumption of compounding annually (n = 1).
#15000 = #800000(1 + 0.1/1)^(1t)
Simplifying the equation:
15/800 = 1.1^t
To solve for t, we will take the logarithm on both sides of the equation to isolate t:
log(15/800) = log(1.1^t)
Using logarithmic properties, we can pull down the exponent:
log(15/800) = t * log(1.1)
Now, divide both sides of the equation by log(1.1) to solve for t:
t = log(15/800) / log(1.1)
Calculating this using a calculator or software:
t ≈ 23.15 years
Therefore, it will take approximately 23.15 years for an investment of #800000, with an annual interest rate of 10%, to grow to #15000.
The length of time for #800000 to earn #15000 if invested at 10% per annum is 15 years.
This can be calculated using the formula:
Time (in years) = (15000 / 800000) x 100 / 10
Time (in years) = 15
To calculate the length of time it takes for #800000 to earn #15000 at an annual interest rate of 10%, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount (P + interest)
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time in years
In this case,
P = #800000
A = P + #15000 = #815000
r = 10% = 0.1 (expressed as a decimal)
n = 1 (interest is compounded annually)
Let's calculate the time it takes to reach #815000:
815000 = 800000(1 + 0.1/1)^(1*t)
Divide both sides by 800000:
815000/800000 = (1.1)^t
1.01875 = 1.1^t
Now, take the natural logarithm (ln) of both sides of the equation to solve for t:
ln(1.01875) = ln(1.1^t)
Using a calculator, calculate the natural logarithm:
t * ln(1.1) = ln(1.01875)
Divide both sides by ln(1.1):
t = ln(1.01875) / ln(1.1)
Using a calculator, calculate the division:
t ≈ 10.98
Therefore, it will take approximately 10.98 years for #800000 to earn #15000 at an annual interest rate of 10%.