Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $9238

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 = $9238 – $6200 = $3038

Thus, Simple Interest = $3038

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 × 3038}/_{6200 × 7}

= ³⁰³⁸⁰⁰/₄₃₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6200

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

Simple Interest = $3038 (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 $6200

= ⁷/₁₀₀ × 6200

= ^{7 × 6200}/₁₀₀

= ⁴³⁴⁰⁰/₁₀₀ = 434

Thus, simple Interest for 1 year = $434

Now,

∵ If the simple Interest is $434, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₄ years

∴ If the simple Interest is $3038, then the time = ¹/₄₃₄ × 3038 years

= ^{1 × 3038}/₄₃₄ years

= ³⁰³⁸/₄₃₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(2) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.

(4) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.