A $3,500.00 principal earns 3% annual interest, compounded semiannually (twice per year). After 20 years, what is the balance in the account?

A. $7,700.00

B. $4,713.99

C. $3.696.00

D. $10,296.00

Principal amount = $3,500.00

Annul interest rate = 3%

Numbers of years = n = 20,

compounded semiannually

Solution:

Use the semiannual compounding period to express the effective semiannual rate which is 3%/2 = 1.5% per 6 month period.

Now there are n=2 (no. of years) semiannual periods for given cash flow

n=2*20

n=40 semiannual periods

Now,

F=P (F/P, 1.5%,40)

F=$3500 (1.8140), (1.8140 is the value get from table at 1.5% interest for n=40)

F=6,349.00 is the amount in bank after 20 years, compounded semiannually.

You can also do this problem by another method which is first find the compound interest by using the formula I = ((1+i/n) ^n) - 1 ... 3 i=3%=0.03 n=20 So, by putting values in the above formula 3, you get I = (1+0.03/20) ^20-1 I=1.031-1 I=0.030403 I=3.043% F=P (F/P, i%, n) F=$3500 (F/P, 3.043,20) When you use this interest (I) then you will need interpolation if the I value is not in the economics table F=6,349.00 The answer will remain same as get by above method.