Question

I need help understanding and finding the answer to number 13

Answer 1

The formula used to calculate the total amount at the end of the period is given to be:

`A=P(1+(r)/(n))^(nt)`

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

t = time in decimal years.

From the question, we have the following parameters:

`\begin{gathered} P=3000 \\ r=1.25\%=0.0125 \\ t=4 \\ n=2\text{ \lparen compounded semi-annually\rparen} \end{gathered}`

Therefore, we can solve the final amount as follows:

`\begin{gathered} A=3000(1+(0.0125)/(2))^(2\cdot4)=3000(1.00625)^8 \\ \therefore \\ A=3153.32 \end{gathered}`

The interest will be calculated to be:

`\begin{gathered} I=A-P \\ I=3153.32-3000=153.32 \end{gathered}`

Therefore, the final amount is $3,153.32.

The interest is $153.32.