Answer:
[tex]\$20,400[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
step 1
Find the rate of interest
in this problem we have
[tex]t=4\ years\\ P=\$18,000\\ A=\$21,600\\r=?[/tex]
substitute in the formula above and solve for r
[tex]\$21,600=\$18,000(1+4r)[/tex]
[tex]1.2=(1+4r)[/tex]
[tex]4r=1.2-1[/tex]
[tex]r=0.2/4=0.05[/tex]
The rate of interest is [tex]5\%[/tex]
step 2
Find the sum of money that will amount to 25,500 in 5 years, at the same rate of interest
in this part we have
[tex]t=5\ years\\ P=?\\ A=\$25,500\\r=0.05[/tex]
substitute in the formula above and solve for P
[tex]\$25,500=P(1+0.05*5)[/tex]
[tex]P=\$25,500/(1.25)=\$20,400[/tex]
