MATH SOLVE

3 months ago

Q:
# 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. $7,700.00B. $4,713.99C. $3.696.00D. $10,296.00

Accepted Solution

A:

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.

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.