Question

General Computers Inc. purchased a computer server for $58,500. It paid 35.00% of the value as a down payment and received a loan for the balance at 7.50% compounded semi-annually. It made payments of $2,050.27 at the end of every quarter to settle the loan. a. How many payments are required to settle the loan? o payments Round up to the next payment

b. Fill in the partial amortization schedule for the loan, rounding your answers to two decimal places.

Answer 1

Answer a:

Number of payments 23 payments

Working:

Loan amount = Cost * (1 - Down payment as %) = 58500 * (1 + 35%) = $38,025

Interest rate (compounded semiannually) = 7.50%

Effective annual rate = (1 + 7.50%/ 2)^2 - 1 = 7.640625%

Quarterly rate = (1 + 7.640625) ^(1/4) -1 = 1.857744%

Given that:

PV = 38025

PMT = 2050.27

Quarterly interest rate = 1.857744%

Hence:

Number of payments = NPER( 1.857744%, 2050.27, -38025, 0, 0) = 22.95 or 23

Answer b:

Payment number 1:

Payment = $2050.27

Interest portion = 38025 * 1.857744% = $706.41

Principal portion = 2050.27 - 706.41 =1343.86

Principal balance = 38025 - 1343.86 = $36,681.14

Similarly we calculate below details for all payment numbers.

Amortization schedule for loan is as follows:

Payment Number Payment BLOC valueNA $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $2,050.27 $1,946.77 Interest Principal Principal Portion Portion Balance $38,025.00 $706.41 $1,343.86 $36,681.14 $681.44 $1,368.83 $35,312.31 $656.01 $1,394.26 $33,918.05 $630.11 $1,420.16 $32,497.89 $603.73 $1,446.54 $31,051.35 $576.85 $1,473.42 $29,577.93 $549.48 $1,500.79 $28,077.15 $521.60 $1,528.67 $26,548.48 $493.20 $1,557.07 $24,991.41 $464.28 $1,585.99 $23,405.42 $434.81 $1,615.46 $21,789.96 $404.80 $1,645.47 $20,144.49 $374.23 $1,676.04 $18,468.45 $343.10 $1,707.17 $16,761.28 $311.38 $1,738.89 $15,022.39 $279.08 $1,771.19 $13,251.20 $246.17 $1,804.10 $11,447.10 $212.66 $1,837.61 $9,609.49 $178.52 $1,871.75 $7,737.74 $143.75 $1,906.52 $5,831.22 $108.33 $1,941.94 $3,889.28 $72.25 $1,978.02 $1,911.26 $35.51 $1,911.26 ($0.00) NINE

Payment for Payment number 23, is derived amount to get principal balance = $0