compounded weekly. If the original amount deposited was , how much interest will she have
earned after 10 years?

10. Mr. and Mrs. Rainer took out a loan to purchase their home. If the interest rate on
the loan is compounded bimonthly, how much interest will they have paid after 30 years?

Ask by Mccarthy Harrington. in the United States

Mar 13,2025

Question

compounded weekly. If the original amount deposited was , how much interest will she have
earned after 10 years?

10. Mr. and Mrs. Rainer took out a loan to purchase their home. If the interest rate on
the loan is compounded bimonthly, how much interest will they have paid after 30 years?

Ask by Mccarthy Harrington. in the United States

Mar 13,2025

UpStudy AI · Accepted Answer

Para resolver el problema de interés compuesto, utilizaremos la fórmula del monto acumulado $$ A $$ en una inversión con interés compuesto:

$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

donde:
- $$ A $$ es el monto total después del tiempo $$ t $$,
- $$ P $$ es el capital inicial (monto depositado),
- $$ r $$ es la tasa de interés anual (en forma decimal),
- $$ n $$ es el número de veces que se capitaliza el interés por año,
- $$ t $$ es el número de años.

### Problema 1: Interés ganado después de 10 años

**Datos:**
- $$ P = 500 $$
- $$ r = 0.0653846 $$ (tasa de interés)
- $$ n = 52 $$ (capitalización semanal)
- $$ t = 10 $$

Sustituyendo los valores en la fórmula:

$$
A = 500 \left(1 + \frac{0.0653846}{52}\right)^{52 \times 10}
$$

Ahora, calculamos el monto $$ A $$ y luego el interés ganado $$ I $$:

$$
I = A - P
$$

### Problema 2: Interés pagado después de 30 años

**Datos:**
- $$ P = 240,000 $$
- $$ r = 0.012 $$ (tasa de interés)
- $$ n = 6 $$ (capitalización bimestral)
- $$ t = 30 $$

Sustituyendo los valores en la fórmula:

$$
A = 240,000 \left(1 + \frac{0.012}{6}\right)^{6 \times 30}
$$

Calcularemos ambos montos $$ A $$ y luego el interés pagado $$ I $$:

$$
I = A - P
$$

Ahora procederé a realizar los cálculos.
Calculate the value by following steps:
- step0: Calculate:
  $$240000\left(1+\left(\frac{0.012}{6}\right)\right)^{6\times 30}$$
- step1: Divide the terms:
  $$240000\left(1+\frac{1}{500}\right)^{6\times 30}$$
- step2: Add the numbers:
  $$240000\left(\frac{501}{500}\right)^{6\times 30}$$
- step3: Multiply the numbers:
  $$240000\left(\frac{501}{500}\right)^{180}$$
- step4: Simplify:
  $$240000\times \frac{501^{180}}{500^{180}}$$
- step5: Rewrite the expression:
  $$500\times 480\times \frac{501^{180}}{500^{180}}$$
- step6: Reduce the numbers:
  $$480\times \frac{501^{180}}{500^{179}}$$
- step7: Rewrite the expression:
  $$20\times 24\times \frac{501^{180}}{500^{179}}$$
- step8: Rewrite the expression:
  $$20\times 24\times \frac{501^{180}}{20^{179}\times 25^{179}}$$
- step9: Reduce the numbers:
  $$24\times \frac{501^{180}}{20^{178}\times 25^{179}}$$
- step10: Rewrite the expression:
  $$8\times 3\times \frac{501^{180}}{20^{178}\times 25^{179}}$$
- step11: Rewrite the expression:
  $$8\times 3\times \frac{501^{180}}{4^{178}\times 5^{178}\times 25^{179}}$$
- step12: Rewrite the expression:
  $$2^{3}\times 3\times \frac{501^{180}}{2^{356}\times 5^{178}\times 25^{179}}$$
- step13: Reduce the numbers:
  $$3\times \frac{501^{180}}{2^{353}\times 5^{178}\times 25^{179}}$$
- step14: Multiply the fractions:
  $$\frac{3\times 501^{180}}{2^{353}\times 5^{536}}$$
Calculate or simplify the expression $$ 500 * (1 + (0.0653846 / 52))^(52 * 10) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$500\left(1+\left(\frac{0.0653846}{52}\right)\right)^{52\times 10}$$
- step1: Divide the terms:
  $$500\left(1+\frac{326923}{260000000}\right)^{52\times 10}$$
- step2: Add the numbers:
  $$500\left(\frac{260326923}{260000000}\right)^{52\times 10}$$
- step3: Multiply the numbers:
  $$500\left(\frac{260326923}{260000000}\right)^{520}$$
- step4: Simplify:
  $$500\times \frac{260326923^{520}}{260000000^{520}}$$
- step5: Rewrite the expression:
  $$500\times \frac{260326923^{520}}{250000^{520}\times 1040^{520}}$$
- step6: Rewrite the expression:
  $$500\times \frac{260326923^{520}}{500^{1040}\times 1040^{520}}$$
- step7: Reduce the numbers:
  $$1\times \frac{260326923^{520}}{500^{1039}\times 1040^{520}}$$
- step8: Multiply the fractions:
  $$\frac{260326923^{520}}{500^{1039}\times 1040^{520}}$$
### Cálculos Realizados

1. **Interés ganado después de 10 años:**
   - Monto acumulado $$ A $$:
   $$
   A \approx 961.07
   $$
   - Interés ganado $$ I $$:
   $$
   I = A - P = 961.07 - 500 \approx 461.07
   $$

2. **Interés pagado después de 30 años:**
   - Monto acumulado $$ A $$:
   $$
   A \approx 343875.41
   $$
   - Interés pagado $$ I $$:
   $$
   I = A - P = 343875.41 - 240000 \approx 103875.41
   $$

### Resultados Finales

- **Interés ganado después de 10 años:** aproximadamente $$ \$ 461.07 $$.
- **Interés pagado después de 30 años:** aproximadamente $$ \$ 103875.41 $$.
Después de 10 años, la persona ganará aproximadamente \$461.07 de interés. Después de 30 años, Mr. y Mrs. Rainer pagarán aproximadamente \$103,875.41 de interés.

compounded weekly. If the original amount deposited was , how much interest will she have
earned after 10 years?

10. Mr. and Mrs. Rainer took out a loan to purchase their home. If the interest rate on
the loan is compounded bimonthly, how much interest will they have paid after 30 years?

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compounded weekly. If the original amount deposited was , how much interest will she have earned after 10 years? 10. Mr. and Mrs. Rainer took out a loan to purchase their home. If the interest rate on the loan is compounded bimonthly, how much interest will they have paid after 30 years?

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Related Questions

Latest Arithmetic Questions

compounded weekly. If the original amount deposited was , how much interest will she have
earned after 10 years?

10. Mr. and Mrs. Rainer took out a loan to purchase their home. If the interest rate on
the loan is compounded bimonthly, how much interest will they have paid after 30 years?