Question

Emily recently started a part time job. She is saving for a car, which she will need when she attends college next year. She plans to deposit $400 at the end of each month into an account that 3.6% per year, compounded monthly . How much will Emily have saved at the end of six months? pays​

Answer 1

$2418.07

Explanation:

Problems involving the time-value of money are conveniently solved using a TVM app on a suitable calculator or spreadsheet. The result of doing that is shown in the attachment.

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If you would like to compute the value of Emily's account by hand, the annuity formula is the one you want.

A = Pn((1 +r/n)^(nt) -1)/r . . . . where r is the annual interest rate, n is the number of times per year it is compounded (12), t is the number of years (1/2), and P is the periodic payment into the acccount (400).

Using the given values in the formula, we have ...

A = 400(12)((1 +0.036/12)^(12/2) -1)/0.036 = 4800×(1.003^6 -1)/0.036

A ≈ 2418.07

At the end of 6 months, Emily will have saved $2418.07.