1. Even though you have no idea who you will marry, you are planning to have an elaborate wedding 4 years from now. The estimated cost of the wedding is $52,000 and you expect to earn 3.5 percent on your savings. How much do you need to save each month for this purpose assuming that you have no money saved as of today?

2. Marcus, Inc. purchased a rare coin for $219,000 three years ago. Today, they resold that coin for $297,500.What annual rate of return did the firm earn on this investment?

(1) $9,973.15

(2) 10.7%

Explanation:

(1) A = P(1+r)^n

A (estimated cost of the wedding) is the total amount to be saved = $52,000

r = interest rate = 3.5% = 0.035

n = duration of savings = 4 years = 4×12 = 48 months

52000 = P(1+0.035)^48

52000 P(1.035)^48

52000 = P(5.214)

P = 52000/5.214 = 9,973.15

Amount to be saved each month is $9,973.15

(2) A = P(1+r)^n

A is the total amount the coin was resold = $297,500

P is the amount the coin was purchased = $219,000

n is the duration of the investment = 3 years

297,500 = 219,000(1+r)^3

(1+r)^3 = 297,500/219,000

(1+r)^3 = 1.358

1+r = (1.358)^1/3

1+r = 1.107

r = 1.107 - 1 = 0.107 = 10.7%

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