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8. The mathematics of savings 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 (1) 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? O FV = PV" X(1 + i) O FV = PV X(1 + i) x 1 O FV = (PVX)" FV = PV X(1 + i)" Now let's use these fundamental concepts to answer questions involving several different situations. Periods 4.50% 5.50% Interest Factors 6.00% 6.50% 7.00% 1.5036 1.5540 1.6058 7.50% 8.00% 8.50% 5.00% 1.4071 9.00% 7 1.3609 1.4547 1.6590 1.7136 1.8280 8 1.4775 1.5347 1.5938 1.6550 1.7835 1.4221 1.4861 1.7182 1.8385 1.8509 1.9990 1.7701 1.9205 2.0839 1.9926 2.1719 9 1.5513 1.7626 1.9172 1.6191 1.7000 10 1.6289 1.6895 1.7906 1.8983 1.8771 1.9672 2.0610 2.1589 2.2610 1.5530 1.6229 2.3674 11 1.9992 2.1049 2.2156 2.3316 2.5804 1.7103 1.7959 1.8021 1.8832 12 1.6959 2.0122 2.1291 2.5182 2.8127 2.2522 2.4098 2.4532 2.6617 2.8879 3.3134 13 1.7722 2.1329 2.2675 1.8856 1.9799 2.3818 2.5604 2.7524 1.9865 2.0961 2.7196 2.9372 1.8519 2.4149 2.5718 15 3.0656 3.3417 3.6425 3.9703 2.5785 2.7590 2.9522 3.1722 2.2609 2.3966 2.5404 2.6928 16 2.7390 1.9353 2.0224 2.1134 2.2085 2.3079 2.0789 2.1829 2.2920 2.4066 2.5270 2.9589 3.1808 3.4194 3.6758 17 3.3997 3.6887 4.0023 3.1588 18 2.8543 2.9170 3.1067 3.3086 3.3799 2.2114 2.3553 2.4848 2.6215 2.7656 2.9178 3.0782 3.2475 3.4262 4.3425 4.7116 19 3.9515 4.2479 3.4259 3.7000 3.9960 4.3157 4.6610 5.0338 5.4365 5.8715 20 4.3276 4.7171 5.1417 5.6044 6.1088 5.1120 3.0256 3.2071 3.3996 3.6035 3.8197 2.4117 2.5202 2.6337 2.6533 2.7860 21 3.6165 3.8697 4.1405 4.4304 4.7405 3.5236 3.7527 4.5664 22 4.9089 2.9253 3.0715 3.9966 4.2564 5.5466 6.0180 6.5296 6.6586 7.2579 23 2.7522 5.2771 Raphael On Raphael's first birthday, his parents deposited $2,000 into a savings account that earns a fixed rate of 5.00% and compounds interest annually. How much money will Raphael's account have accumulated by his 20th birthday? (Hint: Round your answer to the nearest dollar.) O $3,582 O $20,000 O $6.051 O $6,414 What If Scenario 1 What would have been the balance in Raphael's account if his parents had waited until his 10th birthday to make their initial deposit into the same account? $6,414 O $6,051 O $20,000 O $3,582 What If Scenario 2 accumulate an 20th birthday, then should olace deposit on If Raphael's parents wanted his first birthday? O $9,772 O $5,457 O $1.750 O $5,784 Grade It Now Save & Continue Continue without saving