College Algebra Project: Saving for the Future

Good Essays
1983 Words
Grammar
Plagiarism
Writing
Score
College Algebra Project: Saving for the Future
College Algebra Project
Saving for the Future
In this project you will investigate compound interest, specifically how it applies to the typical retirement plan. For instance, many retirement plans deduct a set amount out of an employee’s paycheck. Thus, each year you would invest an additional amount on top of all previous investments including all previously earned interest. If you invest P dollars every year for t years in an account with an interest rate of r (expressed as a decimal) compounded n times per year, then you will have accumulated C dollars as a function of time, given by the following formula.

Compound Interest Formula, with Annual Investments:

FG1 + r IJ LM1 − FG1 + r IJ P H n K MN H n K C (t ) = F rI 1 − G1 + J H nK n n

nt

OP PQ

I will derive this formula to give you a broader understanding of where it came from and how it is based upon the single deposit compound interest formula.

If you invest P dollars every year for t years at an interest rate r, expressed as a decimal, compounded n times per year, then you will have accumulated the cumulative amount of C dollars given by the formula derived bellow: Each annual investment would grow according to the compound interest formula:

F rI A(t ) = PG 1 + J H nK

nt

Here A(t) is the amount that each deposit would be worth at the end of t years. Thus the first deposit of P dollars would draw interest for the full t years, the second deposit would only draw interest for t-1 years, the third deposit would only draw interest for t-2 years… and the last deposit would only draw interest for a single year. Thus we need to add up each deposit and their respectively gained interest values, resulting in the following:

F rI C (t ) = P G 1 + J H nK

nt

FG r IJ LMFG1 + r IJ + FG1 + r IJ + FG1 + r IJ +K+FG1 + r IJ b g + FG1 + r IJ b g OP H n K MNH n K H n K H n K H n K H n K PQ F r I LF r I + FG1 + r IJ + FG1 + r IJ +K+FG1 + r IJ + 1OP, note: FG1 + r IJ = PG 1 + J MG 1 + J H n K

You May Also Find These Documents Helpful

• Good Essays

Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not provided for retirement in-come, and he wants to set up a periodic savings plan to do this. If he makes equal annual payments into a savings account that pays 4 percent interest per year, how large must his payments be to ensure that after retirement he will be able to draw \$30,000 per year from this account until he is 80?…

• 1564 Words
• 7 Pages
Good Essays
• Satisfactory Essays

1.) Find the compound interest on P1,000 at the end of 8 ½ years at 8% compounded quarterly.…

• 2297 Words
• 10 Pages
Satisfactory Essays
• Good Essays

• 488 Words
• 2 Pages

The following formula gives you the total amount one will get if compounding is done:-…

• 488 Words
• 2 Pages
Good Essays
• Good Essays

Example 1: A \$1,000 deposit is made at a bank that pays 12% compounded annually. How much will you have in your account at the end of 10 years?…

• 1158 Words
• 5 Pages
Good Essays
• Satisfactory Essays

* Compound Interest: Interest calculated for a given segment of time of the investment. For example, compounded monthly, means the interest is calculated each month and combined with the principal. So, for the next month, interest is earned on the interest.…

• 380 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

The Present value formula is P =A (1+r)-n where P is the present value that will amount to A dollars in n years at interest rate r compounded annually.…

• 257 Words
• 2 Pages
Satisfactory Essays
• Better Essays

CAT formulae

• 1701 Words
• 7 Pages

I = Interest, P is Principle, A = Amount, n = number of years, r is rate of interest…

• 1701 Words
• 7 Pages
Better Essays
• Satisfactory Essays

where n = number of years. 16 = 10(1 + 0.12 × 5) Glen Arnold, Corporate Financial Management, 5th Edition © Pearson Education Limited 2013 Slide 4.3 Compound interest An investment of £10, an interest rate of 12 per cent. In one year the capital will grow by 12 per cent to £11.20.…

• 1946 Words
• 35 Pages
Satisfactory Essays
• Good Essays

For semi-annual compounding [or for deposits every six months in an annuity], take the annual interest rate and divide it by 2. Take the number of years and multiply by 2.…

• 1397 Words
• 6 Pages
Good Essays
• Satisfactory Essays

• Compound Rate of Return - Understand the compounding effect of interest on investments. ("Calculating internal rate,")…

• 525 Words
• 3 Pages
Satisfactory Essays
• Powerful Essays

Solution Manual

• 9347 Words
• 38 Pages

Compound interest results when the interest paid on the investment during the first period is added to the principal and during the second period the interest is earned on the original principal plus the interest earned during the first period.…

• 9347 Words
• 38 Pages
Powerful Essays
• Satisfactory Essays

This module or note is created to provide students with step-by-step explanation and discussion on time value of money that mainly based on formulas instead of time value of money tables. The reason is so that students are able to answer all sorts of questions that involve interest rates and time period that are not available in the tables.…

• 472 Words
• 2 Pages
Satisfactory Essays
• Good Essays

Compounding of interest occurs when an amount is deposited into a savings account and the interest paid after the specified time period remains in the account, thereby becoming part of the principal for the following period. The general equation for future value in year n (FVn) can be expressed using the specified notation as follows:…

• 1547 Words
• 7 Pages
Good Essays
• Satisfactory Essays

compounded yearly. At the end of 10 years, how much money will be in the savings…

• 283 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

5. How much will \$1,000 deposited in a savings account earning a compound annual interest rate of…

• 3915 Words
• 16 Pages
Satisfactory Essays