How much have you saved and how much more do you need? 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 = PV (1+i) xt FV = (PV i)" FVPV" (1+i) FVPV (1+i)" Future Value Factors Future Value Formula Interest Factors Periods 4.50% 7 1.3609 1.4071 5.00% 5.50% 1.4547 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 1.5036 1.5540 8 1.4221 1.4775 1.5347 1.5938 1.6550 9 1.4861 1.5513 1.6191 1.6895 1.7626 10 1.5530 1.6289 1.7000 1.7908 1.8771 11 1.6229 1.7103 1.8021 1.8983 1.9992 12 1.6959 1.7959 1.8832 2.0122 2.1291 13 1.7722 1.8856 1.9868 2.1329 2.2675 14 1.8519 1.9799 15 1.9353 2.0789 2.2114 2.0961 2.2609 2.3966 2.4149 1.6058 1.6590 1.7182 1.7835 1.8509 1.9206 1.9926 1.8385 1.9172 1.9990 2.0839 2.1719 1.9672 2.0610 2.1589 2.2610 2.3674 2.1049 2.2156 2.3316 2.4532 2.5804 2.2522 2.3818 2.5182 2.6617 2.8127 2.4098 2.5604 2.7196 2.8879 3.0658 2.5785 2.7524 2.9372 3.3134 3.3417 1.7138 1.7701 1.8280 2.5718 2.7590 2.9589 3.1722 3.3997 3.6425 16 2.0224 17 2.1134 2.2920 2.1829 2.3553 2.4848 2.5404 2.7390 2.9522 3.1808 3.4259 3.6887 3.9703 18 2.2085 2.4066 2.6215 2.6928 2.9170 3.1588 2.8543 3.1067 3.3799 3.4194 3.6758 3.7000 4.0023 4.3276 3.9960 4.3425 4.7171 19 2.3079 2.5270 2.7656 3.0256 3.3086 3.6165 3.9515 4.3157 4.7116 5.1417 20 2.4117 2.6533 2.9178 3.2071 3.5236 3.8697 4.2479 4.6610 5.1120 5.6044 21 2.5202 2.7860 3.0782 3.3996 3.7527 4.1406 4.5664 5.0338 5.5466 6.1088 22 23 2.6337 2.7522 2.9253 3.2475 3.6035 3.9966 4.4304 4.9089 5.4365 6.0180 6.6586 3.0715 3.4262 3.8197 4.2564 4.7405 5.2771 5.8715 6.5296 7.2579 Future Value Factors Future Value Formula FV = CFN (1 + i) where FV = future value N = the point in time of the cash flow CFN = single cash flow at time N i = interest rate Charles On Charles's first birthday, his parents deposited $12,000 into a savings account that earns a fixed rate of 8.50% and compounds interest annually. By Charles's 21st birthday, his account will have accumulated $ (Hint: Round your answer to the nearest cent.) What-If Scenario If Charles's parents had waited until his 10th birthday to make their initial deposit of $12,000 into the same account, by Charles's 21st birthday, the balance would have been $ (Hint: Round your answer to the nearest cent.)