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9. Charles River Kayakers (CRK) is renting space at the Museum of Science to store the kayaks that it uses for Boston Harbor expeditions. CRK has agreed to pay $1000 per month for 5 months beginning on May 1. What is the value of the contract on January 1st of the same year

Respuesta :

Based on the interest and the amount paid per month, the value of the contract to Charles River Kayakers (CRK) on January 1st is $4,574.

What is the value of the contract?

The full question assumes a rate of 1.5% per month. Seeing as the payment is constant, the amount is an annuity.

The present value of an annuity due is:

= Amount x ( 1 - ( 1 + rate) ^ -number of periods) / rate x ( 1 + rate)

Solving gives:

= 1,000 x ( 1 - ((1 + 1.5%)⁻⁵) / 1.5%) x (1 + rate)
= $4,854

Then you need to find the present value of this amount in January:

= 4,854 / ( 1 + 1.5%)⁴

= $4,574

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