Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7750

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

$7750 = P (1 + 5% × 5)

⇒ $7750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7750 = P (1 + ²⁵/₁₀₀)

⇒ $7750 = P (^{100 + 25}/₁₀₀)

⇒ $7750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7750

⇒ P = ⁷⁷⁵⁰/_¹²⁵/100

⇒ P = 7750 × ¹⁰⁰/₁₂₅

⇒ P = ^{7750 × 100}/₁₂₅

⇒ P = ⁷⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 7750, then the Principal = ¹⁰⁰/₁₂₅ × 7750

= ^{100 × 7750}/₁₂₅

= ⁷⁷⁵⁰⁰⁰/₁₂₅

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?

(4) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(9) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.