Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8700

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

$8700 = P (1 + 4% × 5)

⇒ $8700 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8700 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8700 = P (1 + ²⁰/₁₀₀)

⇒ $8700 = P (^{100 + 20}/₁₀₀)

⇒ $8700 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8700

⇒ P = ⁸⁷⁰⁰/_¹²⁰/100

⇒ P = 8700 × ¹⁰⁰/₁₂₀

⇒ P = ^{8700 × 100}/₁₂₀

⇒ P = ⁸⁷⁰⁰⁰⁰/₁₂₀

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 8700, then the Principal = ¹⁰⁰/₁₂₀ × 8700

= ^{100 × 8700}/₁₂₀

= ⁸⁷⁰⁰⁰⁰/₁₂₀

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(5) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(8) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.