What is the standard compound interest formula?

What is the standard compound interest formula?

• A. A = P(1 + r)^(t)
• B. A = P(1 + r/n)^(nt)
• C. A = P e^(rt)
• D. A = P + rt

Answer: (B)

Interest grows by multiplying the current balance by a factor each time it’s compounded. When interest is compounded n times per year, the per-period rate is r/n and there are nt periods in t years, so the balance becomes A = P(1 + r/n)^{nt}. This form is the standard because it covers any compounding schedule through n. If you compound annually (n = 1), it reduces to A = P(1 + r)^t. If you compound continuously, the limit of this expression as n grows without bound leads to A = P e^{rt}. The simple-interest formula A = P + rt is a different, linear growth model that doesn’t account for compounding.

Interest grows by multiplying the current balance by a factor each time it’s compounded. When interest is compounded n times per year, the per-period rate is r/n and there are nt periods in t years, so the balance becomes A = P(1 + r/n)^{nt}. This form is the standard because it covers any compounding schedule through n. If you compound annually (n = 1), it reduces to A = P(1 + r)^t. If you compound continuously, the limit of this expression as n grows without bound leads to A = P e^{rt}. The simple-interest formula A = P + rt is a different, linear growth model that doesn’t account for compounding.