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When Gerardo was born, his grandparents started a savings account for him with a beginning balance of 1,250 Peruvian Sols. Every month they deposited 160 Sols into the account. The savings account paid an annual interest rate of 2.1%, compounded monthly.Gerardo just turned 24 and the balance of his account is now $61,917.43.How much of the money in Gerardo's account was earned in interest?(Round your answer to two decimal places, and don't include a currency sign.)

Question

When Gerardo was born, his grandparents started a savings account for him with a beginning balance of 1,250 Peruvian Sols. Every month they deposited 160 Sols into the account. The savings account paid an annual interest rate of 2.1%, compounded monthly.Gerardo just turned 24 and the balance of his account is now $61,917.43.How much of the money in Gerardo's account was earned in interest?(Round your answer to two decimal places, and don't include a currency sign.)

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Solution

Para resolver este problema, sigamos los siguientes pasos:

  1. Calcular el número total de meses: Gerardo tiene 24 años, y cada año tiene 12 meses. Total de meses=24 an˜os×12 meses/an˜o=288 meses \text{Total de meses} = 24 \text{ años} \times 12 \text{ meses/año} = 288 \text{ meses}

  2. Calcular el monto total depositado sin intereses: Los abuelos de Gerardo depositaron 160 Soles cada mes durante 288 meses, además del saldo inicial de 1,250 Soles. Monto total depositado=1,250+(160×288) \text{Monto total depositado} = 1,250 + (160 \times 288) Monto total depositado=1,250+46,080=47,330 Soles \text{Monto total depositado} = 1,250 + 46,080 = 47,330 \text{ Soles}

  3. Calcular el monto total en la cuenta con intereses: El saldo final de la cuenta es 61,917.43 Soles.

  4. Calcular el monto ganado en intereses: Intereses ganados=Saldo finalMonto total depositado \text{Intereses ganados} = \text{Saldo final} - \text{Monto total depositado} Intereses ganados=61,917.4347,330=14,587.43 Soles \text{Intereses ganados} = 61,917.43 - 47,330 = 14,587.43 \text{ Soles}

Por lo tanto, el monto de dinero en la cuenta de Gerardo que fue ganado en intereses es 14,587.43.

This problem has been solved

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