Loan amortisation and sinking funds

2 free worked examples

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1. Exam FMLoan amortisation and sinking fundsCore

   A 250,000 loan is repaid with level annual payments over 20 years at 5.5% effective. Find the annual payment.

   1. A$12,500.00$
   2. B$18,000.00$
   3. C$20,919.83$
   4. D$22,000.00$
   5. E$25,000.00$

   Solution

   1. The loan equals the present value of the payments: $L=P{a}_{\overline{n}|i}$.
   2. $a_{\overline{20}|0.055}=11.950382$.
   3. $P=\frac{250,000}{11.950382}$.
   4. $=20,919.83$. Total payments come to 418,397 against a 250,000 loan, so interest is about 168,000.
2. Exam FMLoan amortisation and sinking fundsExam level

   A 40,000 loan at 8% is repaid with level annual payments over 10 years. Find the interest portion of the FIRST payment.

   1. A$2,239.60$
   2. B$3,200.00$
   3. C$4,000.00$
   4. D$5,961.16$
   5. E$6,000.00$

   Solution

   1. The first payment's interest is charged on the full original balance.
   2. $I_1=L\times i=40,000\times 0.08$.
   3. $=3,200$.
   4. The payment is $40,000/a_{\overline{10}|0.08}=5,961.16$, so the principal portion is $2,761.16$.

   Trap. Applying the general formula when the first payment's interest is simply L·i - much faster.