4C Savings Plans and Investments

# 4C Savings Plans and Investments - Savings Plans and...

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Unformatted text preview: Savings Plans and Investments Wednesday February 2, 2011 (continued) The Savings Plan Formula For most people, depositing a large lump sum of money into an interest bearing account is not feasible. Instead, most people make small monthly payments into an interest bearing account. Suppose you deposit \$100 into an account that pays interest at 12% per year compounded monthly. The following table gives monthly information about the account balance and the interest payments. End of Month Prior balance Interest on Prior Balance End-of- Month Balance New Balance 1 \$ 0 \$ 0 \$100 \$100 2 \$100 1% × \$100 = \$1 \$100 \$201 3 \$201 1% × \$201 = \$2 . 01 \$100 \$303.01 4 \$303.01 1% × \$303 . 01 = \$3 . 03 \$100 \$406.04 5 \$406.04 1% × \$406 . 04 = \$4 . 06 \$100 \$510.10 6 \$510.10 1% × \$510 . 10 = \$5 . 10 \$100 615.20 Suppose we wanted to to calculate the balance of the account after month 217. We could extend the table to have 217 rows, or we could use the following formula. Example 1. Using the Savings Plan Formula Use the savings plan formula to calculate the balance after 6 months for an APR of 12% and monthly payments of \$100 Solution We have monthly payments of PMT = \$100, annual interest rate of APR = 0.12, n = 12 because the payments are made monthly, and Y = 1/2 because 6 months is a half year. Using the savings formula, we can find the balance after 6 months. A = PMT × 1 + APR n nY- 1 APR n = \$100 × 1 + . 12 12 12 × 1 / 2- 1 . 12 12 = \$100 × [(1 . 01) 6- 1] . 01 = \$615 . 20 1 2 A = PMT × 1 + APR n nY- 1 APR n A = accumulated savings plan balance PMT = regular payment (deposit) amount APR = annual percentage rate(as a decimal) n = number of payment periods per year Y = number of years Table 1: Savings Plan Formula (Regular Payments) Example 2. Retirement Plan At age 30 you start an IRA to save for retirement. She deposits \$100 at the end of each month. If you can count on an APR of 6%, how much will you have to you retire 35 years later at age 65? Compare this to the total deposit amount over the 35 years. Solution Use the savings plan formula with payments of PMT = \$100, an interest rate of APR = 0.06, and n = 12 for monthly deposits. THe balance after Y = 35 years is A = PMT × 1 + APR n nY- 1 APR n = \$100 × 1 + . 06 12 12 × 35- 1 . 06 12 = \$100 × [(1 . 005) 420- 1] . 005 = \$142 , 471 . 03 To calculate the total deposit amount over the 35 years, note that there are 35...
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4C Savings Plans and Investments - Savings Plans and...

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