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 $9440 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $9440

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 = $9440 – $5900 = $3540

Thus, Simple Interest = $3540

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 × 3540}/_{5900 × 6}

= ³⁵⁴⁰⁰⁰/₃₅₄₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3540 (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 $3540, then the time = ¹/₃₅₄ × 3540 years

= ^{1 × 3540}/₃₅₄ years

= ³⁵⁴⁰/₃₅₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(3) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

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

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(8) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.