Question

37. Mathewr desires $360,000 in 16 years. He has a choice of several different investments, all of which earn 13%. Each investment will be compounded on a different basis. How much does he need to invest today? (Four separate questions of equal weight) a. Investment #1, compounded annually. b. Investment #2, compounded semi-annually. C. Investment #3, compounded quarterly d. Investment #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.

360,000=P*(1.13)^16

P=360,000/(1.13)^16

=360,000*0.141496242

=$50938.65(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.

360,000=P*(1+0.13/2)^(2*16)

P=360,000/(1+0.13/2)^(2*16)

=360,000*0.133294599

=$47986.06(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.

360,000=P*(1+0.13/4)^(4*16)

P=360,000/(1+0.13/4)^(4*16)

=360,000*0.129132672

=$46487.76(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.

360,000=P*(1+0.13/12)^(12*16)

P=360,000/(1+0.13/12)^(12*16)

=360,000*0.126335521

=$45480.79(Approx)