Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $11390

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 = $11390 – $6700 = $4690

Thus, Simple Interest = $4690

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 × 4690}/_{6700 × 7}

= ⁴⁶⁹⁰⁰⁰/₄₆₉₀₀

= 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) = $6700

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

Simple Interest = $4690 (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 $6700

= ⁷/₁₀₀ × 6700

= ^{7 × 6700}/₁₀₀

= ⁴⁶⁹⁰⁰/₁₀₀ = 469

Thus, simple Interest for 1 year = $469

Now,

∵ If the simple Interest is $469, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₉ years

∴ If the simple Interest is $4690, then the time = ¹/₄₆₉ × 4690 years

= ^{1 × 4690}/₄₆₉ years

= ⁴⁶⁹⁰/₄₆₉ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(5) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.

(9) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.