Answer to Question #121337 in Financial Math for Danelle Sammy

Question

7)Find and compare the future value after two years of a deposit of $100 attracting interest at a rate a) annually and b) semiannually.
8)Which will deliver a higher future value after one year, a deposit of $1, 000 attracting interest at 15% compounded daily, or at 15.5% compounded semi-annually?
9)What initial investment subject to annual compounding at 12% is needed to produce $1, 000 after two years?
10)Which will deliver a higher future value after one year, a deposit of $1, 000 attracting interest at 15% compounded daily, or at 15.5% compounded semi-annually?
11)What initial investment subject to annual compounding at 12% is needed to produce $1, 000 after two years?
12)Find the present value of $100, 000 to be received after 100 years if the interest rate is assumed to be 5% throughout the whole period and a) daily or b) annual compounding applies.

Answer 1

7)

$FV=100(1+0.1)^2=121$

$FV=100(1+\frac{0.1}{2})^4=121.55$

once every six months more

8)

$FV=1000(1+\frac{0.15}{365})^{365}=1161.79$

$FV=1000(1+\frac{0.155}{2})^{2}=1 161.00$

accrued daily will give more

9)

$1000=PV(1+0.12)^2=797.19$

10)

$FV=1000(1+\frac{0.15}{365})^{365}=1161.79$

$FV=1000(1+\frac{0.155}{2})^{2}=1 161.00$

accrued daily will give more

11)

$1000=PV(1+0.12)^2=797.19$

12)

a)

$100 000=PV(1+\frac{0.05}{365})^{36500}=673.93$

b)$100 000=PV(1+{0.05}^{100}=760.45$