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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 PV=PVx (1+i) xt O PV=PV x (1 + i) O PV = (PVxi)" O FV = PV x (1+i) Periods 4.50% 1.3609 7 8 9 10 11 12 13 14 15. 16 17 18 19 20 21 Rina 22 23 1.4071 1.4221 1.4775 1.4861 1.5513 1.6191 5.00% 5.50% 6.00% 6.50% 7.00% 1.4547 1.5036 1.5540 1.6058 1.6590 1.7138 1.5347 1.5938 1.6550 1.7182 1.7835 1.8509 1.6895 1.7626 1+8385 1.9172 1.9990 1.5530 1.6289 1.7000 1.7908- 1.8771 1.9672 2.0610 2.1589 1.8021 1.8983 1.9992 2.1049 1.8832 2.0122 2.1291 2.2522 1.7722 1.8856 1.9868 2.1329 2.2675 2.4098 1.6229 1.7103 2.2156 2.3818 1.6959 1.7959 2.5604 2.7196 2.4149 2.5785 2.7524 2.9372 1.8519 1.9799 2.0961 2.2609 1.9353 2.0224 2.1829 2.5718 2.7590 2.9589 3.1722 2.0789 2.2114 2.3553 2.9522 2.1134 2.2920 3.1588 2.2085 2,4066 2.6215 2.8543 3.3799 2.3079 2.5270 2.7656 3.0256 3.6165 5.1417 2.4117 2.6533 3.2071 3.8697 4.2479 4.6610 5.1120 5.6044 2.5202 2.7860 3.0782 4.5664 6.1088 3.3996 4.1406 5.0338 5.5466 2.6337 2.9253 3.2475 3.6035 3.9966 4.4304 4.9089 5.4365 6.0180 2.7522 3.0715 3.4262 3.8197 4.2564 4.7405 5.2771 5.8715 6.5296 7.2579 6.6586 Interest Factors 2.3966 2.5404 2.4848 2.6928 2.9178 2.7390 2.9170 3.1067 3.3086 3.5236 3.7527 7.50% 8.00% 8.50% 9.00% 1.7701 1.8280 1.9206 1.9926 2.0839 2.1719 2.2610 2.3674 2.580 2.3316 2,4532 2.5182 2.6617 2.8127 2.8879 3,0658 3.3134 3.3417 3.3997 3.6425 3.1808 3.4259 3.6887 3.9703 3.4194 3.7000 4.0023 4.3276 3.6758 3.9960 4.3425 3.9515 4.3157 4.7116 4.7171 On Rina's first birthday, her parents deposited $2,000 into a savings account that earns a fixed rate of 6.00% and compounds interest annually. How much money will Rina's account have accumulated by her 20th birthday? (Hint: Round your answer to the nearest dollar.) U$3,582 O $20,000 O $6,051 O $6,414 What If Scenario 1 What would have been the balance in Rina's account if her parents had waited until her 10th birthday to make their initial deposit into the same account? $6,414 O $3,582 O $20,000 O $6,051 What If Scenario 2 If Rina's parents wanted to accumulate an account balance of $17,500 by her 20th birthday, then how much should they have placed on deposit on her first birthday? O $5,784 O $9,772 O $1,750 O $5.457