Question

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

Answer 1

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.