CFA® Level 1: Compound Interest Calculation

Compound Interest Calculation

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Question

At the end of every year for the next 3 years, you deposit $400 in an account that pays 5% per year, annually compounded. After that, you do not make any more deposits. The amount that you can withdraw after 7 years is:

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A. B. C. D.

A

For the first 3 years, your regular deposits constitute an annuity and after that, a simple term deposit. The future value of an n-period annuity that starts paying at the end of the current period equals FV = (C/r)*[(1+r)^n - 1] where C is the payment per period and r is the one-period interest rate. In this example, the annuity is over 3 periods, C = 400 and the per period rate equals 5%. So the future value of the deposits after 3 years equals (400/0.05)*[1.05^3 - 1] = 1,261. Starting in year

3, this amount grows at an annual rate of 5% for a period of 7-3 = 4 years. So in 7 years, the amount in the account equals 1,261*1.05^4 = $1,533.

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