The interest earned on a savings deposit is a function of four variables - The amount of money held on deposit (PV) - The method to be used in calculating interest-for example, simple versus compound interest - The interest rate applied to the amount on deposit (i) - The frequency with which the account's interest is earned-for example, annually, semiannually, quarterly, monthly, or daily Another important variable is the amount of time during which the funds are held in the savings account (n). These variables and their interaction determine the account's balance at a particular point in time. How do these variables work together to determine an account's balance? Which of the following formulas would you choose to calculate the future balance on an account that earns compound interest? FV=PVn(1+i)FV=(PVi)nFV=PV(1+i)tFV=PV(1+i)n Now let's use these fundamental concepts to answer questions involving several different situations. Interest Factors \begin{tabular}{llllllllllll} \hline Periods & 4.50% & 5.00% & 5.50% & 6.00% & 6.50% & 7.00% & 7.50% & 8.00% & 8.50% & 9.00% \\ 7 & 1.3609 & 1.4071 & 1.4547 & 1.5036 & 1.5540 & 1.6058 & 1.6590 & 1.7138 & 1.7701 & 1.8280 \\ \hline 8 & 1.4221 & 1.4775 & 1.5347 & 1.5938 & 1.6550 & 1.7182 & 1.7835 & 1.8509 & 1.9206 & 1.9926 \\ \hline 9 & 1.4861 & 1.5513 & 1.6191 & 1.6895 & 1.7626 & 1.8385 & 1.9172 & 1.9990 & 2.0839 & 2.1719 \\ 10 & 1.5530 & 1.6289 & 1.7000 & 1.7908 & 1.8771 & 1.9672 & 2.0610 & 2.1589 & 2.2610 & 2.3674 \\ \hline 11 & 1.6229 & 1.7103 & 1.8021 & 1.8983 & 1.9992 & 2.1049 & 2.2156 & 2.3316 & 2.4532 & 2.5804 \\ \hline 12 & 1.6959 & 1.7959 & 1.8832 & 2.0122 & 2.1291 & 2.2522 & 2.3818 & 2.5182 & 2.6617 & 2.8127 \\ 13 & 1.7722 & 1.8856 & 1.9868 & 2.1329 & 2.2675 & 2.4098 & 2.5604 & 2.7196 & 2.8879 & 3.0658 \\ \hline 14 & 1.8519 & 1.9799 & 2.0961 & 2.2609 & 2.4149 & 2.5785 & 2.7524 & 2.9372 & 3.3134 & 3.3417 \\ 15 & 1.9353 & 2.0789 & 2.2114 & 2.3966 & 2.5718 & 2.7590 & 2.9589 & 3.1722 & 3.3997 & 3.6425 \\ \hline 16 & 2.0224 & 2.1829 & 2.3553 & 2.5404 & 2.7390 & 2.9522 & 3.1808 & 3.4259 & 3.6887 & 3.9703 \\ \hline 17 & 2.1134 & 2.2920 & 2.4848 & 2.6928 & 2.9170 & 3.1588 & 3.4194 & 3.7000 & 4.0023 & 4.3276 \\ \hline 18 & 2.2085 & 2.4066 & 2.6215 & 2.8543 & 3.1067 & 3.3799 & 3.6758 & 3.9960 & 4.3425 & 4.7171 \\ \hline 19 & 2.3079 & 2.5270 & 2.7656 & 3.0256 & 3.3086 & 3.6165 & 3.9515 & 4.3157 & 4.7116 & 5.1417 \\ \hline 20 & 2.4117 & 2.6533 & 2.9178 & 3.2071 & 3.5236 & 3.8697 & 4.2479 & 4.6610 & 5.1120 & 5.6044 \\ \hline 21 & 2.5202 & 2.7860 & 3.0782 & 3.3996 & 3.7527 & 4.1406 & 4.5664 & 5.0338 & 5.5466 & 6.1088 \\ \hline 22 & 2.6337 & 2.9253 & 3.2475 & 3.6035 & 3.9966 & 4.4304 & 4.9089 & 5.4365 & 6.0180 & 6.6586 \\ \hline 23 & 2.7522 & 3.0715 & 3.4262 & 3.8197 & 4.2564 & 4.7405 & 5.2771 & 5.8715 & 6.5296 & 7.2579 \\ \hline \end{tabular} On Manuel's first birthday, his parents deposited $7,000 into a savings account that earns a fixed rate of 4.00% and compounds interes much money will Manuel's account have accumulated by his 20th birthday? (Hint: Round your answer to the nearest dollar.) $10,361$15,338$14,748$70,000 What-If Scenario 1 What would have been the balance in Manuel's account if his parents had waited until his 10 th birthday to make their initial deposit int account? $14,748$10,361$15,338$70,000 What-If Scenario 2 If Manuel's parents wanted to accumulate an account balance of $15,000 by his 20 th birthday, then how much should they have placed his first birthday? $10,134$7,120$1,500$6,846
