Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $7590

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

$7590 = P (1 + 3% × 5)

⇒ $7590 = P (1 + ³/₁₀₀ × 5)

⇒ $7590 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7590 = P (1 + ¹⁵/₁₀₀)

⇒ $7590 = P (^{100 + 15}/₁₀₀)

⇒ $7590 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7590

⇒ P = ⁷⁵⁹⁰/_¹¹⁵/100

⇒ P = 7590 × ¹⁰⁰/₁₁₅

⇒ P = ^{7590 × 100}/₁₁₅

⇒ P = ⁷⁵⁹⁰⁰⁰/₁₁₅

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 7590, then the Principal = ¹⁰⁰/₁₁₅ × 7590

= ^{100 × 7590}/₁₁₅

= ⁷⁵⁹⁰⁰⁰/₁₁₅

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(2) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?

(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.