Find the annual interest rate?

Question

A sum of money is put inot a bank account. After 8 years the money has increased by 50% find the annual interest rate.

Answer 1

The problem doesn't say how often interest is accrued; here's a solution when it's once per year.

The formula for compound interest is as follows:

P is the principal (the initial amount you deposit)

r is the annual rate of interest.

n is the number of years the amount is deposited or borrowed for.

A is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

A = P(1 + r)^n

You know the relationship between A and P (the money has increased by 50%) and you know the number of years 'n' (8). From this you can solve for 'r':

A = 1.5P

1.5P = P(1+r)^8
1.5 = (1+r)^8

take the 8th root of both sides:
(1.5)^(1/8) = 1+r

and solve for r:
r=(1.5)^(1/8) - 1

That's the exact solution for r; if you need a decimal approximation, you can just punch that into a calculator. It's a bit less than 5.2%.

Answer 2

The money in the account will equal P x (1+i)^n; where P is the original amount of money, i is the interest rate per compounding period, and n is the number of periods. The interest rate should be expressed as a decimal, rather than the percentage. If the interest rate is 10%, then i = 0.10. Lets use one dollar as the original amount. The final amount = $1.50, so (1+i)^8 = 1.5. Take the 8th root of 1.5 (raise 1.5 to the power of 0.125 on you scientific calculator) and you get 1.05198951 to be equal to (1+i). Subtract out the 1, and i=.05198951, so i = 5.198951%±.

Answer 3

x = 1.5^(1/8) - 1 where x equals the annual interest rate. The 1/8 is the exponent used to take a cumulative rate over 8 years and change it to a one-year rate.

1.5^(1/8) becomes 1.052. Then subtract 1 from this and you get 0.052. Multiply by 100 and you get 5.2% as the annual interest rate.

And people wonder why over 25 developed countries are kicking our butts in math!

Answer 4

NO distinction, purely different time body. you're counting days as each and each and every and compounding quarterly. APR is figured at even 30day periods. that throws accessible 4 extra days each and every 3 years and 5 extra days each and every 4th 12 months. Thats as close as i receives for you. i do no longer have a monetary calculator the following at abode and do not sense like getting a paper a pen to do your homework. in case you imagine we are incorrect and also you're good then WHY contained in the hell waste the time to submit.

Answer 5

Not really possible to answer if you don't know the frequency of compounding. There is a difference if the money is compounded daily, monthly, quarterly, or annually.

Answer 6

5.1980517%