Question

What amount invested today would grow to $10,100 after 20 years, if the investment earns: (Do not round intermediate calculations and round your final answers to 2 decimal places.) Amount $ a. 4% compounded annually b. 4% compounded semiannually c. 4% compounded quarterly d. 4% compounded monthly

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

10100=P*(1.04)^20

P=10100/(1.04)^20

=$4609.51(Approx).

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

10100=P*(1+0.04/2)^(2*20)

P=10100/(1+0.04/2)^(2*20)

=10100*0.452890415

=$4574.19(Approx).

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

10100=P*(1+0.04/4)^(4*20)

P=10100/(1+0.04/4)^(4*20)

=10100*0.451117939

=$4556.29(Approx)

d.We use the formula:
A=P(1+r/12)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

10100=P*(1+0.04/12)^(12*20)

P=10100/(1+0.04/12)^(12*20)

=10100*0.449927139

=$4544.26(Approx).