Respuesta :
The interest rate would be 3.98% when compounded quarterly. Given the data, the interest rate is r₂ = 4%. As everything else remains the same let us use the formula
A( quarterly) = A (Semiannually)
[tex]P(1+\frac{r1}{n1}) ^{n1t} =P( 1+ \frac{r2}{n2}) ^{n2t}[/tex]
Simplifying the equations we get:
[tex](1+\frac{ri}{n1}) ^{n1} = (1+\frac{r2}{n2}) ^{n2}[/tex]
Substituting n1 = 4 (quarterly:) and n2 = 2(semiannually)
Then [tex](1+\frac{ri}{4}) ^{4} = (1+\frac{0.04}{2}) ^{2}[/tex]
[tex](1+\frac{ri}{4}) ^{2} =1.02[/tex]
[tex](1+\frac{ri}{4}) =1.009950[/tex]
[tex]\frac{r_{1}}{4}[/tex] = 0.009950
[tex]r_{1}[/tex] = 0.03980
[tex]r_{1}[/tex] = 3.98%
There are various types in which compounding can be done like monthly, quarterly, semiannually, annually, and continuously compounding.
The factors that will affect the amount of compound interest will be:
(1) The principal amount
(2) the interest rate
(3) The time period
(4) |The type of compounding
(5) The interest of the previous amount.
1. Learn more about compounded annually here:
https://brainly.com/question/15478106
2. Learn more about semiannually here:
https://brainly.com/question/14704604
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