Question

Unknown to you, your grandmother started depositing $25 (out of her social security checks) each month, beginning the day you were born. Your grandmother died on your twentieth birthday, but left you the passbook. You found out that the bank maintained monthly compounding for all 20 years, but the interest rate had changed as follows: (a) Date of your birth to fifth birthday = 0.04; (b) Beginning fifth birthday to fifteenth birthday = 0.08; (c) Beginning fifteenth birthday to present = 0.12. How much money can you withdraw from the account on your twentieth birthday? Round your final answer to two decimal places. See Example 6.5 if you haven't already.

Answer 1

Solution:

(i) Calculation of Maturity amount of the savings from your birth to fifth birthday

Following are the steps to be followed on Microsoft Excel:

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.04/12 Nper =5*12 PMT = -25 Type = 1

FV = $1663.00

Calculation of Future value of $1663.00 from your fifth birthday to fifteenth birthday

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.08/12 Nper =10*12 PV = -1663.00 Type = 1

FV = $3691.26

Calculation of Future value of $3691.26 from your fifteenth birthday till present

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.12/12 Nper =5*12 PV = -$3691.26 Type = 1

FV = $6705.90 ----------------------------- A

(ii) Calculation of Maturity amount of the savings from your fifth birthday to fifteenth birthday

Following are the steps to be followed on Microsoft Excel:

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.08/12 Nper =10*12 PMT = -25 Type = 1

FV = $4604.14

Calculation of Future value of $4604.14 from your fifteenth birthday till present

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.12/12 Nper =5*12 PV = -$4604.14 Type = 1

FV = $8364.33 ----------------------------- B

(iii) Calculation of Maturity amount of the savings from your fifteenth birthday till present

Following are the steps to be followed on Microsoft Excel:

Step 1: Click on "FORMULAS" tab at the top of Microsoft Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "FV"
Step 4: Insert Rate = 0.12/12 Nper = 5*12 PMT = -25 Type = 1

FV = $2062.16 ------------------------------- C

Hence, the money that you can withdraw from your bank account on your twentieth birthday

= $6705.90 + $8364.33 + $2062.16

= $17,132.39