On January 1, 2014, Sauder Corporation signed a five-year noncancelable lease fo

Question

On January 1, 2014, Sauder Corporation signed a five-year noncancelable lease for equipment. The terms of the lease called for Sauder to make annual payments of $150,000 at the beginning of each year for five years with the title passing to Sauder at the end of this period. The equipment has an estimated useful life of 7 years and no salvage value. Sauder uses the straight-line method of depreciation for all of its fixed assets. Sauder appropriately accounts for this lease transaction as a capital lease. The minimum lease payments were determined to have a present value of $625,479 at an effective interest rate of 10%. In 2015, Sauder should record interest expense of..?

Explanation / Answer

$52,303.

P = payment
i = period interest rate
n = number of periods or payments to pay off the loan
and A = loan amount

To calculate Ak = the balance after k payments, start with A0 = A


A1 = A(1+i)-P
A2 = A1(1+i)-P
A2 = (A(1+i)-P)(1+i)-P
A2 = A(1+i)2-P(1+i)-P
A3 = A2(1+i)-P
A3 = (A(1+i)-P)(1+i)-P(1+i)-P
A3 = A(1+i)3-P(1+i)2-P (1+i)-P
Ak = A(1+i)k-P(1+i)(k-1)-P (1+i)(k-2)…-P(1+i)-P

Factor out the P
Ak = A(1+i)k-P((1+i)(k-1)+(1+i)(k-2)+…+(1+i)2...

Using Geometric Series Formula (Just google it to find out more about it...CAn't explain it here...)
(1+i)(k-1)+(1+i)(k-2)+…+(1+i)2+(1+i)+1 using the geometric series formula (with x = 1+i)
we get:
(1+i)(k-1)+(1+i)(k-2)+…+(1+i)2+(1+i)+1
= (1-(1+i)k)/(1-(1+i))
= ((1+i)k-1)/i


SO:
Ak = A(1+i)k-P((1+i)k-1)/i

When the loan is paid off, An=0
0 = A(1+i)n-P((1+i)n-1)/i


Solve for A
A = P((1+i)n-1)/(i(1+i)n)
PV = Pmt((1-(1+i)-n))/i

Year Beginning Balance Scheduled Payment Extra Payment Total Payment Principal Interest Ending Balance Cumulative Interest 1                       625,479                           165,000                           -                 165,000           102,452             62,548                523,027                             62,548 2                       523,027                           165,000                           -                 165,000           112,697             52,303                410,330                           114,851 3                       410,330                           165,000                           -                 165,000           123,967             41,033                286,363                           155,884 4                       286,363                           165,000                           -                 165,000           136,363             28,636                150,000                           184,520 5                       150,000                           165,000                           -                 150,000           135,000             15,000                            -                             199,520

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