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A saving account pays 2% interest compounded annually. If $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit?

A saving account pays 2% interest compounded annually. If $1,200 is deposited initially-example-1
User ZerOne
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1 Answer

15 votes
15 votes

Answer:

(d) $3745.93

Explanation:

A sequence of payments made at the beginning of each time period is referred to as an "annuity due." The last payment of such a sequence earns interest for the full period, and each previous payment earns compounded interest for an increasing number of periods.

The future value of an annuity due is the sum of the geometric series of payment values with first term P(1 +r) and common ratio (1 +r), where P is the payment amount and r is the interest rate for the period.

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series sum

The formula for the sum of the geometric series of n payments is ...

FV = P(1 +r)((1 +r)^n -1)/r

application

For the series of payments with P=$1200 and r=0.02, the future value after n=3 time periods is ...

FV = $1200(1.02)((1.02^3 -1)/0.02 ≈ $3745.93

There will be $3745.93 in the account after 3 years.

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Additional comment

Spreadsheets and graphing calculators have functions that will evaluate this formula for you. When using these functions, you need to make sure to indicate you want the value of an annuity due, not an ordinary annuity. The latter assumes payments are made at the end of the period. (The result differs by the factor (1+r).)

User Daantie
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