Question

A deposit of 1,000 is made into an account at the beginning of each year for 30 year and earn 6% interest compounded annually. Witch of the following is closest to the value in the account at the end of thirtieth year ?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: write the given details

`\begin{gathered} P=1000 \\ r=(6)/(100)=0.06 \\ t=30 \\ n=1\text{ since it is compounded annually} \end{gathered}`

STEP 2: Write the formula for compound interest

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

STEP 3: find the compound amount at the end of the 30th year

`\begin{gathered} By\text{ substitution,} \\ A=1000(1+(0.06)/(1))^(1\cdot30) \\ A=1000(1.06)^(30) \\ A=5473.491173 \\ A=\text{ \$}5473.49 \end{gathered}`

Hence, the amount at the end of the 30th year is approximately $5473.49