Ninja question. Does anyone have another approach to solve this problem?
Janet Taylor Casual Wear has $75,000 in a bank account as of December 31, 2007. If the company plans on depositing $4,000 in the account at the end of each of the next three years (2008, 2009, and 2010) and all amounts in the account earn 8% per year, what will the account balance be at December 31, 2010? Ignore the effect of income taxes.
8% Interest Rate Factors
Period Future Value of $1 Future Value of an Annuity of $1
1 1.0800 1.0000
2 1.1664 2.0800
3 1.2597 3.2464
4 1.3605 4.5061
A.$87,000
B. $88,001
C.$96,070
D.$107,464
The correct answer is D.
The problem is set up to enable you to use both the “Future value of $1” factors and the “Future value of an annuity of $1” factors. The initial investment will earn interest for three years (December 31, 2007, until December 31, 2010) and will be factored with a “future value” factor of 1.2597. The three deposits of $4,000 are an annuity of $4,000 for three years. This annuity will use a “future value of an annuity” factor of 3.2464.
Initial Deposit: $75,000 x 1.2597 = $ 94,478
Annuity of $4,000 for 3 years at 8%: $ 4,000 x 3.2464 = $ 12,986
Total account balance at 12/31/10 $107,464
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