Question

# You deposit \$5,000 into an account at the end of year 0. You deposit \$5,000 every...

You deposit \$5,000 into an account at the end of year 0. You deposit \$5,000 every three (3) months beginning at the end of year 1 and continuing through the end of year 3. You also deposit into the account an amount X starting at the end of year 6 and repeat it every three (3) months for a total of four (4) deposits. You withdraw \$112,160 at the end of year 7. After the withdrawal at the end of year 7, there is no more money in the account. The account pays 4% compounded quarterly. What is the amount you must every three (3) months deposit starting at the end of year 6 (value of X)?

 Time(in years) Deposit Amount with interest 0 0.25 0.5 0.75 1 5000 1.25 5000 5050 10050 1.5 5000 10151 15151 1.75 5000 15302 20302 2 5000 20505 25505 2.25 5000 25760 30760 2.5 5000 31068 36068 2.75 5000 36428 41428 3 5000 41843 46843 3.25 47311 47311 3.5 47784 47784 3.75 48262 48262 4 48745 48745 4.25 49232 49232 4.5 49724 49724 4.75 50222 50222 5 50724 50724 5.25 51231 51231 5.5 51743 51743 5.75 52261 52261 6 52783 52783 6.25 53311 53311 6.5 53844 53844 6.75 54383 54383 7 13412 54927 68339 7.25 13412 69022 82434 7.5 13412 83258 96670 7.75 13412 97637 111049 8 112160 112160

On solving via excel we get the value to be \$13,412

**Hope this helped**

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