Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $9375

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

$9375 = P (1 + 5% × 5)

⇒ $9375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9375 = P (1 + ²⁵/₁₀₀)

⇒ $9375 = P (^{100 + 25}/₁₀₀)

⇒ $9375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9375

⇒ P = ⁹³⁷⁵/_¹²⁵/100

⇒ P = 9375 × ¹⁰⁰/₁₂₅

⇒ P = ^{9375 × 100}/₁₂₅

⇒ P = ⁹³⁷⁵⁰⁰/₁₂₅

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = ¹⁰⁰/₁₂₅ × 9375

= ^{100 × 9375}/₁₂₅

= ⁹³⁷⁵⁰⁰/₁₂₅

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(2) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(4) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(7) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(9) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.