Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $6390

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 = $6390 – $4500 = $1890

Thus, Simple Interest = $1890

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 × 1890}/_{4500 × 7}

= ¹⁸⁹⁰⁰⁰/₃₁₅₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4500

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

Simple Interest = $1890 (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 $4500

= ⁷/₁₀₀ × 4500

= ^{7 × 4500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = 315

Thus, simple Interest for 1 year = $315

Now,

∵ If the simple Interest is $315, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₅ years

∴ If the simple Interest is $1890, then the time = ¹/₃₁₅ × 1890 years

= ^{1 × 1890}/₃₁₅ years

= ¹⁸⁹⁰/₃₁₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.