Saving. How much money should be invested monthly at 6% per year, compounded monthly, in order to have $2000 in 8 months?
i = .06/12 =.005
n = 8(12) = 96
P(1.005)^96 = 2000
solve for P
To determine how much money should be invested monthly to have $2000 in 8 months, we need to use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt),
where:
A is the final amount,
P is the principal amount (the amount to be invested monthly),
r is the annual interest rate (in decimal form),
n is the number of times the interest is compounded per year, and
t is the number of years.
In this case, we're looking for the monthly investment amount (P), with an interest rate of 6% per year (0.06), compounded monthly (n = 12), and a time period of 8 months (t = 8/12 = 2/3 years).
Plugging in these values into the formula, we get:
2000 = P(1 + 0.06/12)^(12 * (2/3)).
To solve this equation for P, we can follow these steps:
1. Divide both sides of the equation by (1 + 0.06/12)^(12 * (2/3)).
This gives us: P = 2000 / (1 + 0.06/12)^(12 * (2/3)).
2. Calculate the value of (1 + 0.06/12)^(12 * (2/3)).
This will give us the value to use in the equation.
In this case, it is approximately 1.04705.
3. Substitute this value into the equation and solve for P:
P = 2000 / (1.04705) ≈ $1881.10.
Therefore, to have $2000 in 8 months at a 6% interest rate compounded monthly, you would need to invest approximately $1881.10 per month.