Question

Would you rather have a saving account that pays 5% interest compounded semiannually or one that pays 5% interest compounded quarterly. explain.

If you have $1000 in saving, after one year how much you have in each case?

Show your work.

Answer 1

a.EAR=[(1+APR/m)^m]-1
where m=compounding periods

EAR for 5% interest compounded semiannually=(1+0.05/2)^2-1

=5.0625%

EAR for 5% interest compounded quarterly=(1+0.05/4)^4-1

=5.09%(Approx).

Hence 5% interest compounded quarterly is better having higher EAR.

b.For 5% interest compounded semiannually:

We use the formula:
A=P(1+r/2)^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$1000*(1+0.05/2)^(2*1)

=$1000*1.050625

=$1050.625

For 5% interest compounded quarterly:

We use the formula:
A=P(1+r/4)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$1000*(1+0.05/4)^(4*1)

=$1000*1.050945337

=$1050.95(Approx).