Question

Betty DeRose is going to deposit $2,800 into a savings account at
the beginning of every six months for the next ten years. Assume
the account will earn 20% interest compounded semi-annually.

Calculate the amount of interest Betty DeRose will earn over the
ten year period.

Use the time value of money factors posted in carmen to answer this
question. To access these factors, click modules and then scroll to
week 12. Click on the link labeled present & future value table
factors. No credit will be awarded for this question using a means
other than these table factors to answer this question.

Future Value of a Lump-Sum Rate of interest per period in percent Periods 3% 5% 6% 8% 9% 10% 12% 15% 20% 1.1576 3 1.0151 1.0927 1.1910 1.2597 1.2950 1.3310 1.4049 1.5209 1.7280 1.1255 1.1593 1.1941 4 1.0202 1.2155 1.2625 1.3605 1.4116 1.4641 1.5735 1.7490 2.0736 1.2783 1.3382 1.6105 1.7716 5 1.0253 1.4693 1.5386 1.7623 2.0114 2.4883 1.0304 71.0355 1.5869 2.3131 6 1.3401 1.4185 1.6771 1.9738 2.9860 2.2107 3.5832 1.2299 1.4071 1.5036 1.7138 1.8280 1.9487 2.6600 1.0407 1.2668 1.4775 1.5940 1.8510 1.9926 2.1436 2.4760 3.0590 4.2998 9 1.0459 1.3048 1.5513 1.6895 1.9990 2.1719 2.3579 2.7731 3.5179 5.1598 10 1.0511 1.3439 1.6289 1.7909 2.1589 2.3674 2.5938 3.1059 4.0456 6.1917 3.8960 5.4736 8.9161 12 1.0617 1.4257 1.7959 2.0122 2.5182 2.8127 3.1384 5.3503 2.0789 15 1.0777 1.5580 2.3966 3.1722 3.6425 4.1773 8.1371 15.4070 9.3576 16 1.0831 1.6047 2.1829 2.5404 3.4259 3.9703 4.5950 6.1304 18.4884 3.7000 17 1.0885 1.6529 2.2920 2.6928 4.3276 5.0545 6.8660 10.7613 221861 18 1.0939 1.7024 2.4066 2.8543 3.9960 4.7171 5.5599 7.6900 12.3755 26.6233 3.0256 19 1.0994 1.7535 1.8061 1.8603 2.5270 4.3157 5.1417 6.1159 8.6128 14.2318 31.9480 20 1.1049 2.6533 2.7860 3.2071 4.6610 5.6044 6.7275 9.6463 16.3665 38.3376 5.0338 6.1088 21 1.1104 3.3996 7.4002 10.8038 18.8215 46.0051 22 1.1160 1.9161 2.9253 3.6035 5.4365 6.6586 8.1403 12.1003 21.6447 55.2061 5.8715 23 1.1216 1.9736 3.0715 3.8197 7.2579 8.9543 13.5523 24.8915 66.2474 1.1272 2.0325 24 3.2251 4.0489 6.3412 7.9111 9.8497 15.1786 28.6252 79.4969 2.0938 25 1.1328 3.3864 4.2919 6.8485 8.6231 10.8347 17.0001 32.9190 95.3962 60 1.3489 5.8916 18.6792 32.9877 101.257 176.031 304.482 897.597 4383.99 56347.5 Present Value of a Lump-Sum Rate of interest per period in percent 9% Periods 12% 0.7118 3% 5% 6% 8% 10% 15% 20% 3 0.9852 0.9151 0.8638 0.8396 0.7938 0.7722 0.7513 0.6575 0.5787 40.9803 0.8885 0.8227 0.7920 0.7350 0.7084 0.6830 0.6355 0.5718 0.4823 0.7473 0.5674 0.9754 0.8626 0.8375 0.7835 0.6806 0.6499 0.6209 0.4972 0.4019 0.5963 6 0.9705 0.7462 0.7050 0.6311 0.5645 0.5066 0.4323 0.3349 7 0.9657 0.8131 0.7107 0.6651 0.5835 0.5470 0.5132 0.4523 0.3759 0.2791 0.2326 0.3269 0.2843 8 0.9609 0.7894 0.6768 0.6274 0.5403 0.5019 0.4665 0.4039 0.7664 0.4241 0.1938 9 0.9561 0.6446 0.5919 0.5003 0.4604 0.3606 10 0.9514 0.7441 0.6139 0.5584 0.4632 0.4224 0.3855 0.3220 0.2472 0.1615 0.9419 0.7014 0.3971 12 0.5568 0.4970 0.3555 0.3186 0.2567 0.1869 0.1122 0.4173 15 0.9279 0.6419 0.4810 0.3152 0.2745 0.2394 0.1827 0.1229 0.0649 0.1069 16 0.9233 0.6232 0.4581 0.3937 0.2919 0.2519 0.2176 0.1631 0.0541 0.9187 0.9141 17 0.6050 0.4363 0.3714 0.3503 0.2703 0.2311 0.1978 0.1456 0.0929 0.0451 0.5874 0.2503 0.0808 18 0.4155 0.2120 0.1799 0.1300 0.0376 0.1161 0.1037 19 0.9096 0.5703 0.3957 0.3305 0.2317 0.1945 0.1635 0.0703 0.0313 20 0.9051 0.5537 0.3769 0.3118 0.2146 0.1784 0.1486 0.0611 0.0261 0.5375 0.1987 0.1839 21 0.9006 0.3589 0.2942 0.1637 0.1351 0.0926 0.0531 0.0217 0.0181 22 0.8961 0.5219 0.3418 0.2775 0.1502 0.1228 0.0826 0.0462 0.5067 0.4920 0.4776 0.1703 23 0.8917 0.3256 0.2618 0.1378 0.1117 0.0738 0.0402 0.0151 0.8872 0.8828 24 0.3101 0.2470 0.1577 0.1264 0.1015 0.0659 0.0349 0.0126 0.2953 0.1460 25 0.2330 0.1160 0.0923 0.0588 0.0304 0.0105 0.0099 60 0.7414 0.1697 0.0535 0.0303 0.0057 0.0033 0.0011 0.0002 0.0001

Answer 1

Semi Annual Investment	2800
Semi Annual Years	20
Total Investment	56000
Interest Rate	20%

Whatever amount Betty Derose will receive at the end of 10 years will be inclusive of Investment amount of $56,000 & Interest Amount.

Thus Future value of semi annual annuity of $ 2800 is to be calculated.

FV of $1 annuity for 20 Semi annual Years @ 20% = 186.688

FV = 2800 * 186.688 = $522726.40

Interest Portion = 522726.40 - 56000 = $466726.40

However if it is assumed that 20% interest is annual. and half yearly interest comes to 10%, the answer will be as follows:

FV of $1 annuity for 20 Semi annual Years @ 10% = 57.2750

FV = 2800 * 57.2750 = $160,370

Interest Portion = 160,370 - 56000 = $104,370