Question

3.30 Improvements at a Harley-Davidson Plant are estimated to be $7.8 million. Construction is expected to take three years. What is the future worth of the project in year 3 at an interest rate of 6% per year compounded quarterly, assuming the funds are allocated (a) completely at time 0, and (b) equally at the end of each year?

Answer 1

Solution:

The formula for calculating effective annual interest rate is as follows:

$\left ( 1+\frac{r}{m} \right )^{m}-1$

Here,

r is the nominal annual interest rate,

m is number of interest periods per year

The formula for calculating the future worth is as follows:

$F=P(1+i)^{n}$

Here,

P is principal amount,

n is number of years

i is annual rate of interest

The standard nation equation is F=P(F / P , i,n) where the value of the factor is seen in the compound interest factor table.

The formula for calculating the future worth is as follows :

  $F=A\left [ \frac{\left ( 1+i \right )^{n}-1}{i} \right ]$

Here,

A is annual payment

n is number of years

i is annual rate of interest

The standard nation equations is F=A(F / A ,i , n) where the value of the factor is seen in the compound interest factor table.

calculate the effective annual rate of interest as follows:

$i=\left ( 1+\frac{0.06}{4} \right )^{4}-1$

$=\left ( 1.015 \right )^{4}-1$

$=1.06136-1$

  $=0.06136$

$=6.136$ %

a)

Calculating the future worth when funds are allocated lump-sum , as follows:

F= 7,800,000(F / P, 6.136%,3)

= 7,800,000 ( 1.1956)

= $ 9,325,680

Thus the future worth when funds are allocated lump-sum is $ 9,325,680

Calculating the future worth when funds are allocated equally at end of every year, as follows :

$F= \frac{7,800,000}{3}\left ( F / A,6.136 ,3*4 \right )$

= 2600000(3.1878)

= $8,288,280

Thus , the future worth when funds are allocated equally at end of every year is $8,288,280