Question

Need help asap important! thanks so much!

Suppose you deposited $300 in the bank and left it there for 2 years. If the bank

pays 7% interest, compounded each year, how much money would you have at

the end of the 2 years? You may use a calculator. (Hint: Make a chart showing each

year’s balance and interest.)

Answer 1

You would have $343.37 at the end of the 2 years.

Explanation:

Interest earned is like bonus money the bank pays you just for keeping money

`\mathrm{Compund\:Interest\:Formula}:\quad A = P { \left( 1+ ( r )/( n ) \right) }^( nt )`

P: the starting balance of the account (also called initial deposit, or principal)

A: the new balance in the account after N years.

t: the number of years or time

r: the interest rate, (in decimal form)

n: the number of times the interest is compounded each year.

Annually = each year = 1

P =$300, r = 7%, t = 2, n = 1, A = ?

Substitute the numbers into the "Compound Interest Formula".

`A = 300 { \left( 1+ ( 0.07 )/( 1 ) \right) }^( 1 * 2 )`

`\mathrm{Anything\:divided\:by\:1\:gives\:itself}`

`A = 300 { \left( 1+0.07 \right) }^( 1 * 2 )`

`\mathrm{Add\:1\:and\:0.07\:to\:get\:1.07}`

`A = 300 * { 1.07 }^( 1 * 2 )`

`\mathrm{Multiply\:1\:and\:2\:to\:get\:2}`

`A = 300 * { 1.07 }^( 2 )`

`\mathrm{Calculate\:1.07\:to\:the\:power\:of\:2\:and\:get\:1.1449}`

`A = 300 * 1.1449`

`\mathrm{Multiply\:300\:and\:1.1449\:to\:get\:343.47}`

`A = 343.47`

So you would have $343.37 at the end of the 2 years.

Look at the chart

`\mathrm{Year}\quad \mathrm{Year\: Interest}\quad \mathrm{Total\:Interest}\quad \mathrm{Balance}\\\quad1\quad\quad\quad $21.00\quad\quad\quad\quad $21.00\quad\quad\quad\quad $321.00\\\quad2\quad\quad\quad $22.47\quad\quad\quad\quad $43.47\quad\quad\quad\quad $343.47`