Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $6060

Rate of Simple Interest (R) = 4%

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

$6060 = P (1 + 4% × 5)

⇒ $6060 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6060 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6060 = P (1 + ²⁰/₁₀₀)

⇒ $6060 = P (^{100 + 20}/₁₀₀)

⇒ $6060 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6060

⇒ P = ⁶⁰⁶⁰/_¹²⁰/100

⇒ P = 6060 × ¹⁰⁰/₁₂₀

⇒ P = ^{6060 × 100}/₁₂₀

⇒ P = ⁶⁰⁶⁰⁰⁰/₁₂₀

⇒ P = $5050

Thus, the sum borrowed (P) = $5050 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6060, then the Principal = ¹⁰⁰/₁₂₀ × 6060

= ^{100 × 6060}/₁₂₀

= ⁶⁰⁶⁰⁰⁰/₁₂₀

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(2) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.

(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(8) 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.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

(10) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.