Question

$100 at 9% APR compounded
semiannually for 1 year​

Answer 1

The amount at end of 1 year is $ 109.2025

Solution:

Given that,

Principal = $ 100

Rate of interest = 9 % compounded semiannually

Number of years = 1

The formula for total amount using compounded semiannually is:

`A=p\left(1+(r)/(n)\right)^(n t)`

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here,
`r = 9 \% = (9)/(100) = 0.09`

Here, n = 2 since interest is compounded semiannually

Substituting the values in formula,

`A=100\left(1+(0.09)/(2)\right)^(2 * 1)`

`\begin{aligned}&A=100(1+0.045)^(2)\\\\&A=100(1.045)^(2)\\\\&A=100 * 1.092025=109.2025\end{aligned}`

Thus the amount at end of 1 year is $ 109.2025