Answer:
The rate of interest is 2.72%
Step-by-step explanation:
Principal = $12000
Interest = $2880
Amount = Principal + Interest
Amount = 12000+2880
Amount = 14880
Time = 8 years
Formula : [tex]A=P(1+r)^t[/tex]
A = amount
P = Principal
r = rate
t = time
Substitute the values in the formula :
[tex]14880=12000(1+r)^8[/tex]
[tex]\frac{14880}{12000}=(1+r)^8[/tex]
[tex]\sqrt{8}[\frac{14880}{12000}]=(1+r)[/tex]
[tex]1.02725=(1+r)[/tex]
[tex]1.02725-1=r[/tex]
[tex]0.02725=r[/tex]
Rate of interest = 2.72%
Hence the rate of interest is 2.72%
Based on the calculations, you will need to invest $12000 at an interest rate of 2.92%.
Given the following data:
Principal = $12000.
Future value = $2880
Time = 8 year.
Mathematically, compound interest is given by this formula:
[tex]A=P(1+r)^t[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]2880=12000(1+r)^8\\\\(1+r)^8=\frac{2880}{12000} \\\\(1+r)^8=0.24\\\\1+r=\sqrt[8]{0.24} \\\\1+r=3.92\\\\r=3.92-1\\\\[/tex]
r = 2.92%.
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