what must the interest rate be if an investment is to double its value in 15 years, compounded monthly
in decimal form, rounded to 3 significant figures
let the monthly rate be i
(1+i)^180 = 2
1 + i = 2^(1/180) = 1.003858..
so the monthly rate is .3858%
giving us a rate of
4.623 % per annum, compounded monthly
You have $1000 to invest. You place it in a money market fund that pays 8% compounded quarterly. How much will you have in the account at the end on 19 years?
To find the interest rate required for an investment to double its value in 15 years, compounded monthly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment
- P is the principal amount (initial investment)
- r is the interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, we want the investment to double its value, which means the future value (A) should be twice the principal amount (P). Hence, A = 2P.
Now, we can substitute the given values into the formula and rearrange it to solve for the interest rate (r):
2P = P(1 + r/n)^(nt)
Dividing both sides by P:
2 = (1 + r/n)^(nt)
Take the natural logarithm (ln) of both sides:
ln(2) = nt × ln(1 + r/n)
Rearranging the equation to solve for r:
r = (e^(ln(2)/(nt)) - 1) × n
Now, let's plug in the provided values:
n = 12 (monthly compounding, so there are 12 compounding periods per year)
t = 15 years
Using a calculator, we can calculate the value of r:
r = (e^(ln(2)/(12*15)) - 1) × 12
Rounding to three significant figures, the interest rate is approximately 0.047 or 4.7% (in decimal form).