Lesson 13 of 25 · 6 min
Personal loans as a fixed unsecured installment
An unsecured personal loan is a fixed installment whose rate prices a slow recovery.
A personal loan is a fixed installment with no named collateral. Ashmere Personal writes $12,400 at 11.9 percent for 36 months. The payment is $411.27. Total of payments is $14,805.56. Interest over the life is $2,405.56. The formula is Track 22 lesson 2's formula: PMT = P × r × (1+r)^n / ((1+r)^n − 1), with r = 0.119/12 and n = 36.
There is no car and no house in the agreement. Recovery for the lender is slow: there is no pledged asset that can be taken and sold on a stated clock. Track 1 lesson 2 already made that comparison among a card, a mortgage and a pledged portfolio. The personal-loan rate sits above Track 22 lesson 2's car loan because the recovery process is the expensive one in that comparison, not because the installment formula is a different machine.
The installment is still a solved-for remainder. Change P, r or n and the $411.27 moves. What does not appear in the substitution is a collateral mark. Capacity is tested against income and against other claims, a later lesson, not against a pledged asset's value. The rate is the price of that missing pledge.
Same formula as the car. Different recovery. The 11.9 percent is the price of having no named collateral, not a different kind of installment.
Key terms
- Personal loan
- A fixed unsecured installment. No named collateral. Recovery is slow, and the rate prices that.
- Unsecured
- No pledged asset in the agreement. The lender's claim is on the person and the cash-flow, not on a car or a house.
- Interest over the life
- Total of payments minus principal. On this loan, $14,805.56 − $12,400 = $2,405.56.
Worked example
Thirty-six remainders, no pledge
Ashmere Personal. Principal $12,400, illustrative 11.9 percent APR, 36 months. No named collateral.
- Monthly rate r
- 0.00991667
- Installment
- $411.27
- Total of payments
- $14,805.56
- Interest over the life
- $2,405.56
- Named collateral
- None
0.119 ÷ 12.
$12,400 × r × (1+r)^36 / ((1+r)^36 − 1).
The life of the cash schedule.
$14,805.56 − $12,400.
Recovery is slow. The 11.9 percent prices that.
The $411.27 is Track 22's formula on an unsecured principal. The 11.9 percent is Track 1 lesson 2's recovery comparison, written as a rate.
Check yourself
Ashmere Personal writes $9,800 at an illustrative 13.4 percent for 48 months. What is the monthly installment, and what is the total of payments if the printed installment is used for 48 months?
An unsecured personal loan prices recovery that is slow, the comparison Track 1 lesson 2 already made between a card, a mortgage and a pledged portfolio. Open Why a lender lends against securities at all →
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.