Question

Your grandmother has been putting $ 5 000 into a savings account on every birthday since your first​ (that is, when you turned​ 1). The account pays an interest rate of 3 %. How much money will be in the account immediately after your grandmother makes the deposit on your 18th​ birthday? The amount in the account upon your 18th birthday is ​$ nothing. ​(Round to the nearest​ dollar.)

Answer 1

The amount is computed as shown below:

In this question we need to determine the future value as follows:

Future value = Present value (1 + r)ⁿ

Present value is computed as follows:

Present value = Annual payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 5,000 x [ (1 - 1 / (1 + 0.03)¹⁸ ) / 0.03 ]

= $ 5,000 x 13.75351308

= $ 68,767.5654

So, the future value will be computed as follows:

= $ 68,767.5654 x 1.03¹⁸

= $ 117,072 Approximately

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