Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $7762.5

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

$7762.5 = P (1 + 3% × 5)

⇒ $7762.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7762.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7762.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7762.5 = P (^{100 + 15}/₁₀₀)

⇒ $7762.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7762.5

⇒ P = ^7762.5/_¹¹⁵/100

⇒ P = 7762.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7762.5 × 100}/₁₁₅

⇒ P = ⁷⁷⁶²⁵⁰/₁₁₅

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 7762.5, then the Principal = ¹⁰⁰/₁₁₅ × 7762.5

= ^{100 × 7762.5}/₁₁₅

= ⁷⁷⁶²⁵⁰/₁₁₅

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?