Simple Interest
Math MCQs

Question :    Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4255

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4255 = P (1 + 5% × 3)

⇒ $4255 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4255 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4255 = P (1 + ¹⁵/₁₀₀)

⇒ $4255 = P (^{100 + 15}/₁₀₀)

⇒ $4255 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4255

⇒ P = ⁴²⁵⁵/_¹¹⁵/100

⇒ P = 4255 × ¹⁰⁰/₁₁₅

⇒ P = ^{4255 × 100}/₁₁₅

⇒ P = ⁴²⁵⁵⁰⁰/₁₁₅

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4255, then the Principal = ¹⁰⁰/₁₁₅ × 4255

= ^{100 × 4255}/₁₁₅

= ⁴²⁵⁵⁰⁰/₁₁₅

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(2) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.

(4) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(6) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(9) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(10) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.