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Safari File Edit View History Bookmarks window Help 100%, Wed 3:23 PM E account.coachingactuaries.com Manual Chegg Study Guided Solutions and Study Help | Chegg.com how to post a question on cheggs.com -Google Search FM Manual Exit Note an infinite number of amount functions can produce these three effective rates. In this example, a smooth exponential curve exists in year 1, a stock-market type graph in year 2, and a linear function in year 3. Regardless of what occurs during a year, any amount function intersecting these points produces the same three effective rates Introduction Getting Started 1 Interest Measurement 1.1 Interest Rate Definitions Rearrange Formula (1.1.2) to solve for A (t) Amount Function Effective Rate of Interest Present Value & A()-A(t-1) A(t-1) Accumulated Value Effective Rate of Discount Nominal Rate of Interest Nominal Rate of Discount Accumulation Function Summary 1,A (1-1) = A (t) _ A (t-1) i,A (1-1) + A (1-1) = A (1) Using the previous effective interest rates, calculate the time-3 amount function as a function of the time-0 amount function. 1.2 Force of Interest 1.3 All-In-One Relationship Formula A (3) = A (2) (1 + i3) Two Exceptions (Simple Interest and Variable FOI) 1.4 = A (0) (1 t1) (1 + i2) (1 + i3) = 100 (1 . 1) ( 1.1364) (0.72) 1.5 Time Value of Money

Explanation / Answer

i t = A(t) - A(t-1) / A (t-1)

multiplying both sides by A(t-1)

i t A(t-1) = A(t) - A(t-1)

adding A(t-1) on both sides

i t A(t-1) + A(t-1) = A(t)

now on left side we take A(t-1) outside as it is the gcf

A(t-1) ( i t +1 ) = A(t)

or we can write

A(t) = A(t-1) ( 1 + i t )

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