Question

If interest is compounded semi-annually, which expression

represents the account balance in t years?

Answer 1

The equation to represent the account balance in t years

`A\:=\:P\left(1\:+\:(r)/(n)\right)^(2t)`

Explanation:

Given the compound interest equation

`A\:=\:P\left(1\:+\:(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\:+\:(r)/(n)\right)^(nt)`

`A\:=\:P\left(1\:+\:(r)/(n)\right)^(2t)` ∵ n = 2

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

`A\:=\:P\left(1\:+\:(r)/(n)\right)^(2t)`