Simple Interest
Math MCQs

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 & 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) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?

(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?