What is the principal that will grow to $3700 in seven years, five months at 8.8% compounded annually?
The principal that will grow to $3700 in seven years, five months at an annual interest rate of 8.8% compounded annually is approximately $2,334.06.
Understanding Compound Interest Calculation
To find the principal, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the future amount
- P is the principal
- r is the annual interest rate (as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the future amount (A) is given as $3700, the annual interest rate (r) is 8.8% or 0.088, and the time period (t) is 7 years and 5 months, which can be expressed as 7.4167 years.
Substituting these values into the formula, we have:
3700 = P(1 + 0.088/1)^(1 * 7.4167)
Simplifying the equation, we get:
3700 = P(1.088)^(7.4167)
To solve for P, we divide both sides by (1.088)^(7.4167), resulting in:
P = 3700 / (1.088)^(7.4167)
Calculating this value, we find that P ≈ $2,334.06, rounded to the nearest cent.
Therefore, the principal required to grow to $3700 in seven years, five months at an annual interest rate of 8.8% compounded annually is approximately $2,334.06.