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You are saving to buy a $183,000 house
You are saving to buy a $183,000 house. There are two competing banks in your area, both offering certificates of deposit yielding 6.8 percent. How long will it take your initial $100,000 investment to reach the desired level at First Bank, which pays simple interest? (Do not round intermediate calcula decimal places, e.g., 32.16.) Number of years How long will it take your initial $100,000 investment to reach the desired level at Second Bank, which compounds interest monthly? (Do not round intermede answer to 2 decimal places, e.g., 32.16.) Number of years References eBook & Resources Worksheet Learning Objective: 05-04 Explain how interest rates are quoted (and misquoted). Difficulty: 2 Intermediate Section: 5.3 Comparing Rates: The Effect of Compounding Periods Check my work
Expert Solution
Answer : Calculation of number of years when Bank pays on simple interest:
Amount = Principal * Rate * Number of years
183000 = 100000 * 0.068 * Number of years
===> Number of years = 183000 / 6800
= 26.91 years
Calculation of number of years when Bank pays interest compounded monthly:
Rate= 0.068/12= 0.005667
n=[ln(Future Value/PresentValue)]/ln(1+ rate)
= [ln(183000 / 100000)] /ln[1.0056667]
= 106.88 months or 8.91 years
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