# If you invest \$10,000 at 7.74% compounded quarterly for 10 years, what is the maturity value?

Calculate the principal and the interest together, which is called the maturity value (FV).

Step 1: The principal interest rate and term are known.

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If you invest \$10,000 at 7.74% compounded quarterly for 10 years, what is the maturity value?
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Principal: \$10,000

Interest Rate: 7.74% quarterly

Term: 10 years

Step 2: Calculate the periodic interest by applying Formula 9.1.

I= IY/CY=7.74% / 4 = 1.935%= 0.01935

Step 3: Calculate the number of compound periods by applying Formula 9.2.

N= CY x Years= 4×10=40

Step 4: Calculate the maturity value by applying Formula 9.3

FV= PV(1+I) ^N=\$10,000(1+0.01935) ^40 = \$10,000(1.01935) ^40= \$10,000 x 2.152450091=21,524.50

After 10 years, the principal grows to \$21,524.50, which includes your \$10,000 principal and \$11,524.50 of compound interest.

1. Ford Motor Company is considering an early retirement buyout package for some employees. The package involves paying out today’s fair value of the employee’s final year of salary. Shelby is due to retire in one year. Her salary is at the company maximum of \$72,000. If prevailing interest rates are 6.75% compounded monthly, what buyout amount should
Ford offer to Shelby today?

Step 1: The principal interest rate and terms are known.

Principal or PV: \$72,000

Interest Rate: 6.75% monthly

Term: 1 year

Step 2: Calculate the periodic interest by applying Formula 9.1.

I= IY/CY=6.75% / 12 = 0.5625%= 0.005625

Step 3: Calculate the number of compound periods by applying Formula 9.2.

N= CY x Years= 12×1=12

Step 4: Calculate the maturity value by applying Formula 9.3

FV= PV(1+I) ^N=\$72,000(1+0.005625) ^12 = \$72,000(1.005625) ^12= \$72,000 x 1.0696=77,013.21

If prevailing interest rates are 6.75% compounded monthly, the buyout amount that Ford should offer Shelby today is \$77,013.21.

1. Polo Park Bowling Lanes owes the same supplier \$3,000 today and \$2,500 one year from now. The owner proposed to pay both bills with a single payment four months from now. If interest rates are 8.1% compounded monthly, what amount should the supplier be willing to accept?

Take the two lump-sum payments in the future and remove the interest back to today to find the fair amount that Polo Park Bowling Lanes should pay to the supplier. This is the present value (PV).

Step 1: With two amounts and interest rates, there are two time segments. The IY, CY, and Term are identified for each.

Step 2: For each segment, calculate the periodic interest rate by applying Formula 9.1.

Time Segment 1 Time Segment 2

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