Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 10% 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  7

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 10% 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 × 10}

= ⁴⁶⁹⁰⁰⁰/₆₇₀₀₀

= 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) = $6700

Rate of Simple Interest (R) = 10% 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 = 10% of Principal

= 10% of $6700

= ¹⁰/₁₀₀ × 6700

= ^{10 × 6700}/₁₀₀

= ⁶⁷⁰⁰⁰/₁₀₀ = 670

Thus, simple Interest for 1 year = $670

Now,

∵ If the simple Interest is $670, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₇₀ years

∴ If the simple Interest is $4690, then the time = ¹/₆₇₀ × 4690 years

= ^{1 × 4690}/₆₇₀ years

= ⁴⁶⁹⁰/₆₇₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(3) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(6) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?

(9) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.