Question

fernando has $1,608 in an account. the interest rate is 1% compounded annually. to the nearest cent, how much interest will he earn in 5 years? use the formula ( b = p(1 + r)^t ), where ( b ) is the balance (final amount), ( p ) is the principal (starting amount), ( r ) is the interest rate expressed as a decimal, and ( t ) is the time in years.

Explanation:

Step1: Calcular el balance final

Dado que \(p = 1608\), \(r=0.01\) (ya que \(1\%=0.01\)) y \(t = 5\). Sustituimos en la fórmula \(B=p(1 + r)^{t}\).
$$B=1608\times(1 + 0.01)^{5}$$
$$B=1608\times(1.01)^{5}$$
Calculamos \((1.01)^{5}=1.01\times1.01\times1.01\times1.01\times1.01 = 1.0510100501\)
Luego \(B=1608\times1.0510100501\approx1690.02\)

Step2: Calcular el interés

El interés \(I\) se calcula como \(I=B - p\).
Tomando \(B\approx1690.02\) y \(p = 1608\)
$$I=1690.02-1608$$
$$I = 82.02$$

Answer:

\(82.02\)