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 $10540 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $10540

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 = $10540 – $6200 = $4340

Thus, Simple Interest = $4340

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 × 4340}/_{6200 × 7}

= ⁴³⁴⁰⁰⁰/₄₃₄₀₀

= 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) = $6200

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

Simple Interest = $4340 (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 $4340, then the time = ¹/₄₃₄ × 4340 years

= ^{1 × 4340}/₄₃₄ years

= ⁴³⁴⁰/₄₃₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?

(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?