Question

Lowlife Company defaulted on a $190,000 loan that was due on December 31, 2021. The bank has agreed to allow Lowlife to repay the $190,000 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 $27,885 would be required to repay the debt? 4. If three payments of $69,117 are to be made, what interest rate is the bank charging Lowlife?

Answer 1

Required :

1. Annual Payment	$ 59,939
2. Annual Payment	$ 47,587
3.Number of Annual Payments	12
4.Interest Rate	4.5%

Explanation:

1) Here, ( Pv = $ 190,000, I = 10%, N = 4 )

Now, locate the factor using (pvoa $1 table) = 3.16987

Annual Payment = PV ÷ Factor

= $ 190,000 ÷ 3.16987

= $ 59,939

2) Here, ( Pv = $ 190,000 , I = 8% , N = 5)

Now, locate the factor using ( pvoa $1 table ) = 3.99271

Annual Payment = Pv ÷Factor

= $ 190,000 ÷ 3.99271

= $ 47,587.

3) Here, ( Pv = $ 190,000, Annual installment = $ 27,885, I = 10%)

Now, factor would be:

= $ 190,000 ÷ $ 27,885

= 6.81369

Now, locate this factor in 10% coloumn, we will find the same in 12th period row.

Therefore'N = 12.

4) Here, ( Pv = $ 190,000 , Annual installment = $ 69,117, N =3)

Factor would be:

= $ 190,000 ÷ $ 69,117

= 2.74896

Now, locate this factor in 3rd period row, its between 4% and 5%

Real factor	2.74896
At 4%	2.77509
At 5%	2.72325

Both ways it has similiar differece so its around 4.5%