Question

Time Value of Money Problems

Amt./Annuity

PV/FV

1.a. The Lexington Development Co. has a $10,000 note receivable from a customer due in three years. How much is it worth today if the interest rate is 9%?

1.b. How is it worth today if the interest rate is 12% compounded quarterly?

2.a.What will a deposit of $4,500 left in the bank be worth if left in the in the bank for nine years at 7% interest?

2.b.If left for six years at 10% compounded semi-annually?

3.a. According to the Rule of 72, how long will it take $1,000 to double if the interest rate is 8%?

3.b. How long will it take the $1,000 to grow to $16,000? Rule of 72

4.a. What is the value ten years hence of $1,000 invested today at 8% interest, $2,000 invested at the end of year five, and $3,000 invested at the end of year eight?

Answer 1

1 (a). The Lexington Development Co. has a $ 10,000 note receivable from a customer due in three years. How much is it worth today if the interest rate is 9%? Future Value $ 10,000 Interest Rate 9% Period 3 Years Present Value The Value of the Note Receivable on today can be find by bringing the Future Value to the Present Value. This is called as Discounting. Present Value = Future Value (1+r)" $ Future Value Interest Rate (r) Period (n) 10,000 9% 3 Years Present Value = - $ 10,000 (1+0.09) Present Value = $ 7,722 1 (b). How is it worth today if the interest rate is 12% compounded quarterly? If the Interest is compounded Quarterly, Present Value can be found by converting the Rate (r) and Period (n) into No. of Quarters. Future Value $ 10,000 Interest Rate 3.00% Period 12 Quarters Present Value

The Value of the Note Receivable on today can be find by bringing the Future Value to the Present Value. This is called as Discounting. Present Value = Future Value (1+r)" Future Value Interest Rate (0) Period (n) $ 10,000 3% 12 Quarters $ 10,000 Present Value = (1+0.03)12 Present Value = $ 7,014

2 (a).What will a deposit of $4,500 left in the bank be worth if left in the in the bank for nine years at 7% interest? $ Present Value Interest Rate Period Future Value 4,500 7% 9 Years The Value of the Deposit after 9 Years can be find by compounding the Present Value to the Future Value. Future Value = Present Value * (1+r)" $ Present Value Interest Rate (c) Period (n) 4,500 7% 9 Years Future Value = $4,500 * (1+0.07) Future Value = $ 8,273 2 (b). If left for six years at 10% compounded semi-annually? If the Interest is compounded semi-annually, Future Value can be found by converting the Rate (r) and Period (n) into No. of semi-annual periods. Present Value $ 4,500 Interest Rate 5.00% Period 12 Semi-Annual Periods Future Value ? The Value of the Deposit after 9 Years can be find by compounding the Present Value to the Future Value.

Future Value = Present Value * (1+r)" Present Value Interest Rate (0) Period (n) $ 4,500 5% 12 Semi-Annual Periods Future Value = $ 4,500 * (1+0.05)12 Future Value = $ 8,081