Question

6. You are saving for a new house and you put $25,000 per year in an account paying 4.5%. The first payment is made today.

A.) How much will you have at the end of 3 years? (Show Work)

B. Also build a table/schedule to show your account each year (include beginning balance and ending balance each year, interest earned).

Answer 1

Given that I am saving $25,000 each year for 3 years

Rate of interest is 4.5%, lets us assume this rate is annual interest rate

A) Today, I make first payment $25,000

So, for 1^st year, my interest amount = $25000 * 4.5% = $1125

Also, I deposit my payment at beginning of year 1 i.e., $25000

Therefore, at the beginning of year 1, my amount = $25000 + $1125 + $25000 = $51125

So, for 2nd year, my interest amount = $51125 * 4.5% = $2300.625

Also, I deposit my payment at beginning of year 2 i.e., $25000

Therefore, at the beginning of year 2, my amount = $51125+ $2300.625 + $25000 = $78425.625

So, for 3rd year, my interest amount = $78425.625 * 4.5% = $3529.153125

Also, I deposit my payment at beginning of year 3 i.e., $25000

Therefore, at the beginning of year 3 my amount = $78425.625+ $3529.153125+ $25000 = $106954.7781

Interest during the 3^rd year = $106954.7781 * 4.5% = $4812.965016

Therefore total amount at end of 3 years = $106954.7781 + $4812.965016 = $111767.7431

So, amount at the end of 3 years is $111,767.74 (rounded off to two decimals)

B) The below table represents the account for 3 years

	Amount deposited	Opening balance	Interest Per annum (4.5%)	Closing balance
At present	$25000	$25000	$1125	$26125
1st year	$25000	$51125	$2300.625	$53425.625
2nd year	$25000	$78425.625	$3529.153125	$81954.77813
3rd year	$25000	$106954.7781	$4812.965016	$111767.7431