Lowlife Company defaulted on a $250,000 loan that was due on December 31, 2018. The bank has agreed to allow Lowlife to repay the $250,000 by making a series of equal annual payments beginning on December 31, 2019.

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 $51,351 would be required to repay the debt?
4. If three payments of $104,087 are to be made, what interest rate is the bank charging Lowlife?

Explanation:

1. Present value = Annuity amount * PVA (n=4;i=10%)

250,000 = Annuity amount*3.16987

Annuity amount = $78,868

2. Present value = Annuity amount * PVA (n=5;i=8%)

250,000 = Annuity amount* 3.99271

Annuity amount = $62,614

3. i = 10%

Annual payments = $51,351

250,000 = 51,351 *X

X = 4.86845

When looking at the table of present value of an ordinary annuity, PVA of 4.86845 and i=10%, ⇒ n = 7 payments

4.

Payments = 104,087

n = 3

250,000 = 104,087*X

X = 2.40184

When looking at the table of present value of an ordinary annuity, PVA of 2.40184 and n=3, ⇒ i = 12%

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