Si se invierten $5,000, con una tasa de interés de 9% anual, compuesto mensualmente, el valor futuro S en un periodo t (en meses) se obtiene por medio de = 5,000(1.0075)^t a. ¿Cuál es la cantidad después de 1 año? b. ¿Cuánto tiempo pasar antes de que se duplique la inversión?
Answers
Given : $ 5,000 is invested, with an interest rate of 9% per year, compounded monthly, the future value S in a period t (in months) is obtained by means of = 5,000 (1.0075) ^ t
To Find : t for doubling the amount
amount after 1 year
Solution:
P = $ 5000
R = 9 % PA = 0.75 % per month
n = t/12 years = t months
A = 2P = 2 * 5000
A = P(1 + R/100)ⁿ
=> 2 * 5000 = 5000 (1 + 0.75/100)^t
=> 2 = (1.0075)^t
Taking log both sides
=> log 2 = t log (1.0075)
=> 0.3010 = t (0.003245)
=> t = 92.766 months
Approx 93 months to double the investment
amount after 1 year = 5000(1.0075)¹² = $5,469
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