Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $7000

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

$7000 = P (1 + 5% × 5)

⇒ $7000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7000 = P (1 + ²⁵/₁₀₀)

⇒ $7000 = P (^{100 + 25}/₁₀₀)

⇒ $7000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7000

⇒ P = ⁷⁰⁰⁰/_¹²⁵/100

⇒ P = 7000 × ¹⁰⁰/₁₂₅

⇒ P = ^{7000 × 100}/₁₂₅

⇒ P = ⁷⁰⁰⁰⁰⁰/₁₂₅

⇒ 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 = 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 7000, then the Principal = ¹⁰⁰/₁₂₅ × 7000

= ^{100 × 7000}/₁₂₅

= ⁷⁰⁰⁰⁰⁰/₁₂₅

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

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

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

(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.