Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6497.5

Rate of Simple Interest (R) = 3%

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

$6497.5 = P (1 + 3% × 5)

⇒ $6497.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6497.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6497.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6497.5 = P (^{100 + 15}/₁₀₀)

⇒ $6497.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6497.5

⇒ P = ^6497.5/_¹¹⁵/100

⇒ P = 6497.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6497.5 × 100}/₁₁₅

⇒ P = ⁶⁴⁹⁷⁵⁰/₁₁₅

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6497.5, then the Principal = ¹⁰⁰/₁₁₅ × 6497.5

= ^{100 × 6497.5}/₁₁₅

= ⁶⁴⁹⁷⁵⁰/₁₁₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.