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) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(4) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(10) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.