Asking the Bank: a Formal Letter Requesting a Loan

Mutesi, from lesson 1, now writes to her bank. Her business, the bank and the figures are imagined; the interest rate is illustrative.

Mutesi Tailoring
Stall 14, Huye Market
Ngoma Sector, Huye District
1 October 2026

The Branch Manager
Isoko Bank, Huye Branch
Huye

I am writing to apply for a loan of Frw 1,500,000, repayable over 18 months, to buy two machines for my tailoring business. I have held a savings account at your Huye branch since March 2025.

I have run Mutesi Tailoring from Huye Market for five years. Over the past twelve months my earnings have averaged Frw 280,000 a month, as the enclosed statements show. Demand is now greater than I can meet with one domestic sewing machine: this term two secondary schools asked me to make 300 uniforms, and I was able to accept only half of the order.

The loan would be used to buy an industrial sewing machine (Frw 1,150,000) and an overlocking machine (Frw 350,000), according to the enclosed quotation from a supplier in Huye. With them, I expect to double my output and to earn at least Frw 150,000 a month more than I do now. I have also saved Frw 400,000 towards fabric and a second worker's wages for the first two months.

At the rate of 16% a year quoted by your loan officer, the monthly instalment would be about Frw 94,300, which the additional income alone would cover. I am willing to offer the two machines as security, and my uncle, a secondary-school teacher, has agreed to act as my guarantor.

I enclose a copy of my national identity card, my bank statements for the last twelve months, the supplier's quotation, a one-page business plan and a letter from my guarantor. I would welcome the opportunity to discuss this application in person, and I can be reached on the telephone number given in the business plan.

Yours faithfully,

(signature)
MUTESI Claudine

A loan repaid in equal monthly instalments uses this formula, where $PP$ is the amount borrowed, $rr$ the monthly interest rate and $nn$ the number of months:

$$A=P\times \frac{r}{1-(1+r{)}^{-n}}A\; =\; P\; \backslash times\; \backslash frac\{r\}\{1\; -\; (1\; +\; r)^\{-n\}\}$$

For Mutesi: $P=1500000P\; =\; 1\backslash ,500\backslash ,000$, $r=\frac{0.16}{12}\approx 0.013333r\; =\; \backslash frac\{0.16\}\{12\}\; \backslash approx\; 0.013333$, $n=18n\; =\; 18$.

$$A=1500000\times \frac{0.013333}{1-{1.013333}^{-18}}\approx 94284.64A\; =\; 1\backslash ,500\backslash ,000\; \backslash times\; \backslash frac\{0.013333\}\{1\; -\; 1.013333^\{-18\}\}\; \backslash approx\; 94\backslash ,284.64$$

So the instalment is about Frw 94,300. Over 18 months she repays $18\times 94284.64\approx 169712418\; \backslash times\; 94\backslash ,284.64\; \backslash approx\; 1\backslash ,697\backslash ,124$, of which about Frw 197,124 is interest. Her letter states only the instalment, rounded; the officer will give the exact schedule. The point for the writer: never put a number in a formal letter that you have not checked.