Question

If interest is compounded semi-annually, which expression
represents the account balance in t years?

Answer 1

Answer:

The equation to represent the account balance in t years

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}$

Step-by-step explanation:

Given the compound interest equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

here

A represents Accrued Amount (principal + interest)

P represents Principal Amount

I represent Interest Amount

r represents the Annual interest rate

t represents Time Involved in years

n represents the number of compounding periods per unit t

As we are given that the interest is compounded semi-annually

i.e. n = 2

so substituting n = 2 in the equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}$       ∵ n = 2

Thus, the equation to represent the account balance in t years

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}$