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 interestfor example, simple versus compound interest
	The interest rate applied to the amount on deposit (i)
	The frequency with which the accounts interest is earnedfor 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 accounts balance at a particular point in time.

How do these variables work together to determine an accounts 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)nFV=PV(1 + i)n

FV=PV(1+i)tFV=PV1+it

FV=(PVi)nFV=PVin

FV=PVn(1+i)FV=PVn1+i

Now lets use these fundamental concepts to answer questions involving several different situations.

Interest Factors
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
8	1.4221	1.4775	1.5347	1.5938	1.6550	1.7182	1.7835	1.8509	1.9206	1.9926
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
11	1.6229	1.7103	1.8021	1.8983	1.9992	2.1049	2.2156	2.3316	2.4532	2.5804
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
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
16	2.0224	2.1829	2.3553	2.5404	2.7390	2.9522	3.1808	3.4259	3.6887	3.9703
17	2.1134	2.2920	2.4848	2.6928	2.9170	3.1588	3.4194	3.7000	4.0023	4.3276
18	2.2085	2.4066	2.6215	2.8543	3.1067	3.3799	3.6758	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	2.6337	2.9253	3.2475	3.6035	3.9966	4.4304	4.9089	5.4365	6.0180	6.6586
23	2.7522	3.0715	3.4262	3.8197	4.2564	4.7405	5.2771	5.8715	6.5296	7.2579

Rajiv

On Rajivs first birthday, his parents deposited $2,000 into a savings account that earns a fixed rate of 6.00% and compounds interest annually. How much money will Rajivs account have accumulated by his 20th birthday? (Hint: Round your answer to the nearest dollar.)

$6,051

$6,414

$3,582

$20,000

What-If Scenario 1

What would have been the balance in Rajivs account if his parents had waited until his 10th birthday to make their initial deposit into the same account?

$6,051

$3,582

$6,414

$20,000

What-If Scenario 2

If Rajivs parents wanted to accumulate an account balance of $17,500 by his 20th birthday, then how much should they have placed on deposit on his first birthday?

$1,750

$5,784

$5,457

$9,772