noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much…

noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much interest will he earn in 4 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.

noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much interest will he earn in 4 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.

Answer

Explicación:

Paso 1: Identificar los valores de $P$, $r$ y $t$

$P = 4096$, $r=0.14$, $t = 4$

Paso 2: Calcular el saldo final $B$ usando la fórmula $B=P(1 + r)^t$

$B=4096(1 + 0.14)^4=4096\times(1.14)^4$ $(1.14)^4=1.14\times1.14\times1.14\times1.14 = 1.68896016$ $B=4096\times1.68896016=6917.97070536$

Paso 3: Calcular el interés ganado

Interés = $B - P$ Interés = $6917.97070536-4096=2821.97070536\approx2821.97$

Respuesta:

$2821.97$