Assume we invest $2000 for one year in a savings account that pays an APR of 10% compounded quarterly.

Question

Compare the earnings to what simple interest or semiannual compounding would yield.
Earnings with simple interest are $190 and earnings with semiannual compounding are $207.62. Earnings with simple interest are $200 and earnings with semiannual compounding are $207.62. Earnings with simple interest are $200 and earnings with semiannual compounding are $205.62. Earnings with simple interest are $203 and earnings with semiannual compounding are $210.50.

Answer 1

Ivy,

 

In general, the formula for compound interest involves:

 

P(0)=Principal amount in the account at t=0

P(t)=Principal in the account at time = t

t = time in years

n= Number of times the account compounds per year

r= annual interest rate (expressed as a decimal, i.e. 5%=.05)

 

The formula to determine the amount of money in a compounding account at some time t is

 

P(t)=P(0)[1+r/n]^(nt)

 

Or put into words, the amount in the account at any time t is equal to the amount originally in the account times (one plus the annual interest rate divided by the compounding period) raised to the power of (the number of compounding periods per year times the number of years).

 

For compounding quarterly, means that your variables are

P(0)=2000

P(t)=????

t=1

n=4

r=.1

So P(t)=2000(1+.1/4)^4=2207.63, you have 2207.63 in the account after 1 year, and you started with 2000, so you have received 207.63 in interest.

 

If you compound semi-annually, n=2 (not 4), so

2000(1+.1/2)^2=2205.  You have 2205 in the account, and you started with 2000, so you have received 2205-2000=205 in interest.

 

For simply interest (i.e. no compounding), Interest=Prt=2000(.1)(1year)=200

 

You can use these formulas for the other problem you have posted as well.  I hope this helps.  John