Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $7590

Rate of Simple Interest (R) = 2%

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

$7590 = P (1 + 2% × 5)

⇒ $7590 = P (1 + ²/₁₀₀ × 5)

⇒ $7590 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7590 = P (1 + ¹⁰/₁₀₀)

⇒ $7590 = P (^{100 + 10}/₁₀₀)

⇒ $7590 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7590

⇒ P = ⁷⁵⁹⁰/_¹¹⁰/100

⇒ P = 7590 × ¹⁰⁰/₁₁₀

⇒ P = ^{7590 × 100}/₁₁₀

⇒ P = ⁷⁵⁹⁰⁰⁰/₁₁₀

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7590, then the Principal = ¹⁰⁰/₁₁₀ × 7590

= ^{100 × 7590}/₁₁₀

= ⁷⁵⁹⁰⁰⁰/₁₁₀

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(2) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(8) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(10) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?