Question

Lowlife Company defaulted on a $180,000 loan that was due on December 31, 2018. The bank has agreed to allow Lowlife to repay the $180,000 by making a series of equal annual payments beginning on December 31, 2019. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required:

1. Calculate the required annual payment if the bank’s interest rate is 10% and four payments are to be made.
2. Calculate the required annual payment if the bank’s interest rate is 8% and five payments are to be made.
3. If the bank’s interest rate is 10%, how many annual payments of $27,713 would be required to repay the debt?
4. If three payments of $66,097 are to be made, what interest rate is the bank charging Lowlife?
  

Answer 1

Ans:

Lowlife company defaulted on $180,000, loan was due on Dec 31,2018

The Bank has agrees to allow lowlife to repay the $180,000

Present value of Annuity=P(1-(1+r)^(-N) /r)

Where

P =Periodic Payment

R= Rate per period

N=Number of Period

1) The required annual Payment

180,000= P(1-(1+0.1)^(-4) /0.1)

=P(1-0.6831/0.1)

=P(0.31699/0.1)

=3.1699*P

P=180,000/3.1699=$56,784

2) the required annual payment

180,000= P(1-(1+0.08)^(-5) /0.08)

=P(1-0.68058/0.08)

=P(0.31942/0.08)

=3.99275*P

P=180,000/3.99275=$45082

3)The bank interest rate and how many annual Payments

Loan repayment Balance=$180,000

Interest rate=10%

Annual Payment=$27,713

$27,713*PVA of $1(10%,N)=$180,000

PVA of $1(10%,N)=6.4951

Using the present value of annuity N=11

Number of Annual Payments =11

4) The Interest rate is the bank charging lowlife

$66,097*PVA of $1(?%,3)=$180,000

PVA of $1(?%,3)=2.72327

Annuity table i=5%

Annual Interest rate=5%