Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $6985

Rate of Simple Interest (R) = 2%

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

$6985 = P (1 + 2% × 5)

⇒ $6985 = P (1 + ²/₁₀₀ × 5)

⇒ $6985 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6985 = P (1 + ¹⁰/₁₀₀)

⇒ $6985 = P (^{100 + 10}/₁₀₀)

⇒ $6985 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6985

⇒ P = ⁶⁹⁸⁵/_¹¹⁰/100

⇒ P = 6985 × ¹⁰⁰/₁₁₀

⇒ P = ^{6985 × 100}/₁₁₀

⇒ P = ⁶⁹⁸⁵⁰⁰/₁₁₀

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6985, then the Principal = ¹⁰⁰/₁₁₀ × 6985

= ^{100 × 6985}/₁₁₀

= ⁶⁹⁸⁵⁰⁰/₁₁₀

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

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

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(5) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

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

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

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.