Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $6210

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

$6210 = P (1 + 3% × 5)

⇒ $6210 = P (1 + ³/₁₀₀ × 5)

⇒ $6210 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6210 = P (1 + ¹⁵/₁₀₀)

⇒ $6210 = P (^{100 + 15}/₁₀₀)

⇒ $6210 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6210

⇒ P = ⁶²¹⁰/_¹¹⁵/100

⇒ P = 6210 × ¹⁰⁰/₁₁₅

⇒ P = ^{6210 × 100}/₁₁₅

⇒ P = ⁶²¹⁰⁰⁰/₁₁₅

⇒ P = $5400

Thus, the sum borrowed (P) = $5400 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 6210, then the Principal = ¹⁰⁰/₁₁₅ × 6210

= ^{100 × 6210}/₁₁₅

= ⁶²¹⁰⁰⁰/₁₁₅

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(4) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?

(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?