Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9231

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9231 – $5100 = $4131

Thus, Simple Interest = $4131

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4131}/_{5100 × 9}

= ⁴¹³¹⁰⁰/₄₅₉₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4131 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $5100

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = 459

Thus, simple Interest for 1 year = $459

Now,

∵ If the simple Interest is $459, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₉ years

∴ If the simple Interest is $4131, then the time = ¹/₄₅₉ × 4131 years

= ^{1 × 4131}/₄₅₉ years

= ⁴¹³¹/₄₅₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(4) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(6) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.