nate deposited $1,000 in an account earning 5% interest compounded annually. to the nearest cent, how much…

nate deposited $1,000 in an account earning 5% interest compounded annually. to the nearest cent, how much will he have 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.

nate deposited $1,000 in an account earning 5% interest compounded annually. to the nearest cent, how much will he have 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

Dado que $p = 1000$ (monto inicial), $r=0.05$ (tasa de interés del 5% expresada como decimal) y $t = 4$ (años).

Paso 2: Sustituir valores en la fórmula

Sustituimos en la fórmula $B=p(1 + r)^t$, entonces $B = 1000\times(1+0.05)^4$.

Paso 3: Calcular el valor dentro del paréntesis

$1 + 0.05=1.05$.

Paso 4: Calcular la potencia

$(1.05)^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$.

Paso 5: Multiplicar por el principal

$B=1000\times1.21550625 = 1215.50625$.

Paso 6: Redondear al centésimo más cercano

Redondeando $1215.50625$ al centésimo más cercano, obtenemos $1215.51$.

Respuesta:

$1215.51$