Question
In: Economics
*SOLVE IN EXCEL* Sondra deposits $5,500 in an IRA account on April 15, 2019. Assume the...
*SOLVE IN EXCEL*
Sondra deposits $5,500 in an IRA account on April 15, 2019. Assume the account will earn 3% annually. If she repeats this for the next nineteen years (for a total of twenty contributions), how much will she have on deposit on April 14, 2039?
Solutions
Expert Solution
Answer: $ 152,220.67
Excel Table:
| Year | Amount Deposited at April 15 | Balance at April 15 | Interest Rate (%) | Interest on 'Balance at April 15' | Balance at April 14 (of Next Year) |
| 2019 | 5500.00 | 5500.00 | 3% | 165.00 | 5665.00 |
| 2020 | 5500.00 | 11165.00 | 3% | 334.95 | 11499.95 |
| 2021 | 5500.00 | 16999.95 | 3% | 510.00 | 17509.95 |
| 2022 | 5500.00 | 23009.95 | 3% | 690.30 | 23700.25 |
| 2023 | 5500.00 | 29200.25 | 3% | 876.01 | 30076.25 |
| 2024 | 5500.00 | 35576.25 | 3% | 1067.29 | 36643.54 |
| 2025 | 5500.00 | 42143.54 | 3% | 1264.31 | 43407.85 |
| 2026 | 5500.00 | 48907.85 | 3% | 1467.24 | 50375.08 |
| 2027 | 5500.00 | 55875.08 | 3% | 1676.25 | 57551.34 |
| 2028 | 5500.00 | 63051.34 | 3% | 1891.54 | 64942.88 |
| 2029 | 5500.00 | 70442.88 | 3% | 2113.29 | 72556.16 |
| 2030 | 5500.00 | 78056.16 | 3% | 2341.68 | 80397.85 |
| 2031 | 5500.00 | 85897.85 | 3% | 2576.94 | 88474.78 |
| 2032 | 5500.00 | 93974.78 | 3% | 2819.24 | 96794.03 |
| 2033 | 5500.00 | 102294.03 | 3% | 3068.82 | 105362.85 |
| 2034 | 5500.00 | 110862.85 | 3% | 3325.89 | 114188.73 |
| 2035 | 5500.00 | 119688.73 | 3% | 3590.66 | 123279.39 |
| 2036 | 5500.00 | 128779.39 | 3% | 3863.38 | 132642.78 |
| 2037 | 5500.00 | 138142.78 | 3% | 4144.28 | 142287.06 |
| 2038 | 5500.00 | 147787.06 | 3% | 4433.61 | 152220.67 |
Explanation:
Step 1. Amount deposited on April 15, 2019 = $ 5,500. So, Balance on April 15, 2019 = $ 5,500.
Step 2. Interest on this amount @ 3 % = $ 5,500 x 3 / 100 = $ 165.00
Step 3. So, Balance at April 14, 2020 = Balance at April 15, 2019 + Interest on "Balance at April 15, 2019"
= $ 5, 500 + $ 165
Balance at April 14, 2020 = $ 5,665.00
Step 4. Amount deposited on April 15, 2020 = $ 5,500.
So, Balance on April 15, 2020 = Balance at April 14, 2020 + Amount deposited on April 15, 2020
= $ 5,665.00 + $ 5,500.00
Balance on April 15, 2020 = $ 11,165.00
Interest on this amount @ 3 % = $ 11,165 x 3 / 100 = $ 334.95
So, Balance at April 14, 2021 = Balance at April 15, 2020 + Interest on "Balance at April 15, 2020"
= $ 11,165 + $ 334.95
Balance at April 14, 2021 = $ 11,499.95
Step 5. Repeat the step 4 for each year. We get Balance on April 14, 2039 = $ 152,220.67
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