Simple Interest
MCQs Math

Question:     Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8732

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 = $8732 – $5900 = $2832

Thus, Simple Interest = $2832

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 × 2832}/_{5900 × 6}

= ²⁸³²⁰⁰/₃₅₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 6% per annum

Simple Interest = $2832 (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 = 6% of Principal

= 6% of $5900

= ⁶/₁₀₀ × 5900

= ^{6 × 5900}/₁₀₀

= ³⁵⁴⁰⁰/₁₀₀ = 354

Thus, simple Interest for 1 year = $354

Now,

∵ If the simple Interest is $354, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₄ years

∴ If the simple Interest is $2832, then the time = ¹/₃₅₄ × 2832 years

= ^{1 × 2832}/₃₅₄ years

= ²⁸³²/₃₅₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(2) 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?

(3) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(9) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.