Wk5_EYB_Final_Answers.docx

Wk5_EYB_Final_Answers.docx - W5.1 Group Members who worked...

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W5.1 Group Members who worked on this problem: Yuki Suppose that you have $12,500 to invest over a 4 year period. There are two accounts to choose from: 4.5% compounded monthly or 4.3% compounded continuously. a Write the formula for the first account’s compound interest for n compoundings per year. b Write the formula for the account with continuously compounded interest. c Use the formulas and information above to solve for the balance of each investment after 3 years. d Which investment account offers a better return on your money? Calculations Explanations of Calculations 1 a Write the formula for the first account’s compound interest for n compoundings per year. 1 + r n ¿ nt A = P ¿ A is the amount of money in the account with principal, P is the amount of money to invest, r is the annual interest rate, n is the number of compounding per year, and t is the years you invest. For this question, we can use the formula: For n compoundings per year, 1 + r n ¿ nt A = P ¿ ( A is the amount in the account with the principal, P is the money to invest, r is the annual interest rate, t is the years you save the money in the account and n is the number of compoundings per year.) 2 P = 12,500 r = 4.5% =0.045 n = 12 (it compounds every month) t = 4 1 + 0.045 12 ¿ 12 4 A = 12500 ¿ ( answer ) Based on the information obtained from w5.1 monthly compounding, plug those numbers into the formula: 1 + r n ¿ nt A = P ¿ 3 b Write the formula for the account with continuously compounded interest. A = Pe rt A is the amount of money in the account with principal, P is principal money, For this problem, we can use the formula: For continuous compounding, A = Pe rt ( A is the amount in the account
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r is the annual interest rate, t is the years you invest, e is irrational number: the natural base.
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