Question

Lowlife Company defaulted on a $220,000 loan that was due on December 31, 2021. The bank has agreed to allow Lowlife to repay the $220,000 by making a series of equal annual payments beginning on December 31, 2022. (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 $28,924 would be required to repay the debt?
4. If three payments of $77,777 are to be made, what interest rate is the bank charging Lowlife?

Answer 1

Solution 1:

Required annual payment = $220,000 / Cumulative PV factor at 10% for 4 periods

= $220,000 / 3.16987 = $69,403

Solution 2:

Required annual payment = $220,000/ Cumulative PV factor at 8% for 5 periods

= $220,000 / 3.99271 = $55,100

Solution 3:

Let nos of periods required = n

Cumulative PV factor at 10% for n periods = $220,000 / $28,924 = 7.60614

Refer factor table at 10%, this factor falls at n= 15

Therefore it will take 15 years to repay.

Solution 4:

Let interest rate = i

Cumulative PV Factor at i for 3 periods = $220,000 / $77,777 = 2.8286

Refer factor table, this factor falls at 3 period at i =3%