Question

At the beginning of the year, you put $2,000 in a new savings account that has a 3% annual interest rate, but the account earns interest at the end of every six months. At the end of the first year, you withdraw $1,000 from the account.

1. How much interest have you earned after six months? Show your work.

2. How much interest have you earned after one year? Show your work.

3. What is the total amount in your account after two years (remember the withdrawal)? Calculate it two different ways and show your work.

a. Use a simple interest formula to calculate the total amount in your account after two years.

b. Use a compound interest formula to calculate the total amount in your account after two years.

4. How much total interest have you earned after two years? Show and explain.

Answer 1

1)it is given in the question that account earns interest on every six months months it means that it's compounding is on every six months basis.

Amount remain invested for first 6 months.and the rate of interest is 3% p.a.

Amount after 6 months =P(1+i/n)Period =2000(1+.03/2)¹=2030

Amount of interest =2030-2000=30

2)Now after one year there will be two compounding period. And calculation is as follows

Amount after one year =P(1+i/n)^period=2000(1+.03/2)² =2060.45

Interest =2060.45-2000=60.45

3)calculation of amount at the end of first year.

Particulars	compound interest	simple interest
Principal	2000	2000
Amount after on year	P(1+i/2)period	P+(P*R*T/100)
A)	=2000(1+.03/2)2=2060.45	2000+(2000*3*1/100) =2060
B) withdrwal	1000	1000
C)amount left (a-b)	1060.45	1060.00

4)interest for the first year is 60.45 as calculated above and for the second year is calculated below.

Principal for the second year. 1060.45

Amount at the end of second year. =P(1+i/n)^period =1060.45(1+.03/2)² =1092.50

Interest for the second year. =1092.50-1060.45=32.05

Total interest for two year=Interest for first year+interst for second year=60.45+32.05=92.50