Question

1-Automotive Excellence Inc. borrowed $16.000.00 on May 26 with an interest rate of 4,5% per annum. On June 25. $5500.00 was repaid, and on September 18, $5200.00 was repaid. Automotive Excellence paid the balance of the loan on November 24. What was the final payment?

2-What is the present value of​ $3780 due in nine months if interest is​ 5%?

3-What principal will earn​ $34.44 interest at​ 8.25% from May​ 30, 2012, to January​ 4, 2013?

Answer 1

1). Amount borrowed on may 26 = $16,000

Interest rate = 4.5% per annum

On June 25 amount repaid = $5500.00

No of days till June 25 from may 26 = 31 days

Loan balance with interest on June 25  = 16000 +(16000*4.5%*31days/365days)

= $ 16061.15

Loan balance after first repayment = $ 16016.15 - $5500

= $ 10561.15

- On Sept 18 another amount repaid is = $ 5200

No of days till Sept 18 from June 25 = 85days

Loan balance with interest from June 25 to Sept 18 = 10561.15 +(10561.15*4.5%*85days/365days)

= $ 10671.83

Loan balance after second repayment = $ 10671.83 - $5200

= $ 5471.83

- Last repayment is paid on Nov 24

No of days = 61 days

Loan balance with interest of 61 days =5471.83 +(5471.83*4.5%*61days/365days)

= $ 5512.98

So, the final payment = $ 5512.98

2). Calculating the present value of​ $3780 due in nine months if interest is​ 5%:

Monthly rate = 0.05/12 = 0.004166

Present Value = Future value/(1+interest rate)^no of time period

= $ 3780/(1+0.004166)^9

= $ 3641.16

3). No of days between May​ 30, 2012, to January​ 4, 2013 = 220 days

Interest rate = 8.25%

Interest amount = Principal*Interest*no of days/365

34.44 = P*0.0825*220/365

Principal = $ 692.60