Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $6612.5

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

$6612.5 = P (1 + 3% × 5)

⇒ $6612.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6612.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6612.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6612.5 = P (^{100 + 15}/₁₀₀)

⇒ $6612.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6612.5

⇒ P = ^6612.5/_¹¹⁵/100

⇒ P = 6612.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6612.5 × 100}/₁₁₅

⇒ P = ⁶⁶¹²⁵⁰/₁₁₅

⇒ P = $5750

Thus, the sum borrowed (P) = $5750 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 6612.5, then the Principal = ¹⁰⁰/₁₁₅ × 6612.5

= ^{100 × 6612.5}/₁₁₅

= ⁶⁶¹²⁵⁰/₁₁₅

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(2) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) If Donna paid $5432 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 will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?

(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(7) 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?

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.