Question

A bank has lent you $1,000,000 today. You have agreed to pay back $100,000 at the end of each year for 20 years. If you pay back the money as promised, what is the irr on the bank's loan?

Answer 1

Given:

(i) The bank has lent me $10,00,000.

(ii) I will give back $ 1,00,000 at the end of each year.

(iii) Total time = 20 years.

To find:

(i) Rate of interest on bank's loan.

Solution:

Principal money (P), the money lent = $10,00,000

Total money repayed after 20 years (A) = 20*Money paid after each year

= $ (20*100000)

= $ 20,00,000

Let the rate of interest be R% p.a.

So, Simple Interest (SI) = $\frac{PRT}{100}$

= $\frac{1000000*R*20}{100}$

= $ 2,00,000R

We know, total amount (A) is:

A = P + SI

= $ (10,00,000 + 2,00,000R)

This is equal to $ 20,00,000

So,

(10,00,000 + 2,00,000R) = 20,00,000

⇒  2,00,000R = 10,00,000

⇒ R = 10,00,000/2,00,000

⇒ R = 5% p.a

The rate of interest is 5% p.a.

Answer 2

Step-by-step explanation:

Principal money (P), the money lent = $10,00,000

Total money repayed after 20 years (A) = 20*Money paid after each year

= $ (20*100000)

= $ 20,00,000

Let the rate of interest be R% p.a.

So, Simple Interest (SI) = \frac{PRT}{100}

100

PRT

= \frac{1000000*R*20}{100}

100

1000000∗R∗20

= $ 2,00,000R

We know, total amount (A) is:

A = P + SI

= $ (10,00,000 + 2,00,000R)

This is equal to $ 20,00,000

So,

(10,00,000 + 2,00,000R) = 20,00,000

⇒ 2,00,000R = 10,00,000

⇒ R = 10,00,000/2,00,000

⇒ R = 5% p.a

The rate of interest is 5% p.a.