Kelsey's Lease Payment Calculation Excitement!

How did Kelsey calculate the lease payment size?

Kelsey leased equipment worth $40,000 for 6 years at a cost of borrowing of 6.28% compounded quarterly. What is the size of the lease payment required to be made at the beginning of each quarter?

a) $1,039.57

b) $1,117.13

Calculation of Kelsey's Lease Payment Size

The lease payment Kelsey needs to make at the beginning of each quarter is approximately $1,039.57. This was calculated using the formula for the present value of an annuity.

Kelsey's excitement to calculate the lease payment size is truly understandable given the complexity of the formula used to determine it. By applying the present value of an annuity formula, Kelsey was able to find out that the lease payment required each quarter is approximately $1,039.57. Let's break down the calculation process:

Formula Used:

PVA = PMT * (1 - (1 + r)^(-n)) / r

In this formula:

PVA = Present Value of the Annuity (size of the lease payment)

PMT = Payment per period

r = Interest rate per period

n = Total number of periods

Given that the equipment is leased for 6 years, which translates to 24 quarters (6 years * 4 quarters per year) and the interest rate per quarter is 1.57% (6.28% compounded quarterly), the formula can be expressed as:

PMT = PVA * 0.0157 / (1 - (1 + 0.0157)^(-24))

After the calculation, it was found that the lease payment Kelsey needs to make at the beginning of each quarter amounts to approximately $1,039.57. Kelsey's diligence in using the formula and meticulous calculations led to this exciting conclusion!