Al miler, owner of al's garage, estimates that he will need $29,000 for new equipment in 15
years. al decided that he would put aside the money now so that in 15 years the $29,000 will be available. his bank offers him 10 percent interest compounded semiannually. (use the tables in the handbook) al must invest today:
a. $6,710.60
b. $6,942.60
c. $6,701.60
d. $125,335.10
e. none of these

The answer is option A). $6,710.60

Explanation:

The total amount Al miler will need to invest at the beginning to have the money in 15 years is known as the principal amount.

The formula for calculating the total amount after 15 years with interest compounded semiannually is as follows;

A = P (1 + r/n) (nt)

where;

A = the future value of the initial investment

P = initial investment amount/principal amount

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

A=$29,000

P=p

r=10/100=0.1

n=interest is compounded semiannually which is twice a year=2

t=15 years

Replacing values in the formula;

29,000=p(1+0.1/2)^(2×15)

29,000=p(1+0.05)^30

29,000=4.322 p

p=29,000/4.322

p=$6,710

Al must invest $6,710 for him to have enough money for the new equipment in 15 years