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) Assuming an interest rate of 15%

compounding interest formula is as follows;

$FV= PV* (1+r/n){^n}{^t}$

FV is future value

PV is present value

r is interest

n is number of compounding in a year

t is the total number of years

a)compounded annually

$FV= 100 * (1+0.15/1)^{1*2}$

$FV=132.25/$

b) compounded semi-annually

$FV= 100 * (1+0.15/2)^{2*2}$

$FV=133.55/$

8)

a)compounded daily at 15%

$FV= 1,000 * (1+0.15/365)^{365*1}$

$FV=1,161.80$

b) compounded semi-annually at 15.5%

$FV= 1,000 * (1+0.155/2)^{2*1}$

$FV=1,161.01/$

Compounding daily is slightly higher

9)

$1,000= PV* (1+0.12/1)^{2*1}$

$PV=797.19$

10) Is a repetition of question 8

11) Is a repetition of question 9

12)

a)compounded daily

$100,000= PV* (1+0.05/365)^{100*365}$

$PV=674.03/$

b)compounded daily

$100,000= PV* (1+0.05/1)^{100*1}$

$PV=760.45/$