Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7417.5

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

$7417.5 = P (1 + 3% × 5)

⇒ $7417.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7417.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7417.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7417.5 = P (^{100 + 15}/₁₀₀)

⇒ $7417.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7417.5

⇒ P = ^7417.5/_¹¹⁵/100

⇒ P = 7417.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7417.5 × 100}/₁₁₅

⇒ P = ⁷⁴¹⁷⁵⁰/₁₁₅

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 7417.5, then the Principal = ¹⁰⁰/₁₁₅ × 7417.5

= ^{100 × 7417.5}/₁₁₅

= ⁷⁴¹⁷⁵⁰/₁₁₅

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

(2) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(4) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(9) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?