Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $6440

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

$6440 = P (1 + 3% × 5)

⇒ $6440 = P (1 + ³/₁₀₀ × 5)

⇒ $6440 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6440 = P (1 + ¹⁵/₁₀₀)

⇒ $6440 = P (^{100 + 15}/₁₀₀)

⇒ $6440 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6440

⇒ P = ⁶⁴⁴⁰/_¹¹⁵/100

⇒ P = 6440 × ¹⁰⁰/₁₁₅

⇒ P = ^{6440 × 100}/₁₁₅

⇒ P = ⁶⁴⁴⁰⁰⁰/₁₁₅

⇒ P = $5600

Thus, the sum borrowed (P) = $5600 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 6440, then the Principal = ¹⁰⁰/₁₁₅ × 6440

= ^{100 × 6440}/₁₁₅

= ⁶⁴⁴⁰⁰⁰/₁₁₅

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.

(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.