Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $10000

Rate of Simple Interest (R) = 5%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$10000 = P (1 + 5% × 5)

⇒ $10000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $10000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $10000 = P (1 + ²⁵/₁₀₀)

⇒ $10000 = P (^{100 + 25}/₁₀₀)

⇒ $10000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $10000

⇒ P = ¹⁰⁰⁰⁰/_¹²⁵/100

⇒ P = 10000 × ¹⁰⁰/₁₂₅

⇒ P = ^{10000 × 100}/₁₂₅

⇒ P = ^1000000/₁₂₅

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 10000, then the Principal = ¹⁰⁰/₁₂₅ × 10000

= ^{100 × 10000}/₁₂₅

= ^1000000/₁₂₅

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.