Simple Interest
Math MCQs

Question :    Joshua had to pay $5635 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  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5635

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

$5635 = P (1 + 5% × 3)

⇒ $5635 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5635 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5635 = P (1 + ¹⁵/₁₀₀)

⇒ $5635 = P (^{100 + 15}/₁₀₀)

⇒ $5635 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5635

⇒ P = ⁵⁶³⁵/_¹¹⁵/100

⇒ P = 5635 × ¹⁰⁰/₁₁₅

⇒ P = ^{5635 × 100}/₁₁₅

⇒ P = ⁵⁶³⁵⁰⁰/₁₁₅

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5635, then the Principal = ¹⁰⁰/₁₁₅ × 5635

= ^{100 × 5635}/₁₁₅

= ⁵⁶³⁵⁰⁰/₁₁₅

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(3) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?