Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9617

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 = $9617 – $5900 = $3717

Thus, Simple Interest = $3717

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 × 3717}/_{5900 × 7}

= ³⁷¹⁷⁰⁰/₄₁₃₀₀

= 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) = $5900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3717 (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 = 7% of Principal

= 7% of $5900

= ⁷/₁₀₀ × 5900

= ^{7 × 5900}/₁₀₀

= ⁴¹³⁰⁰/₁₀₀ = 413

Thus, simple Interest for 1 year = $413

Now,

∵ If the simple Interest is $413, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₃ years

∴ If the simple Interest is $3717, then the time = ¹/₄₁₃ × 3717 years

= ^{1 × 3717}/₄₁₃ years

= ³⁷¹⁷/₄₁₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?

(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(3) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.