Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11340

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 = $11340 – $6300 = $5040

Thus, Simple Interest = $5040

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 × 5040}/_{6300 × 10}

= ⁵⁰⁴⁰⁰⁰/₆₃₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5040 (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 $6300

= ¹⁰/₁₀₀ × 6300

= ^{10 × 6300}/₁₀₀

= ⁶³⁰⁰⁰/₁₀₀ = 630

Thus, simple Interest for 1 year = $630

Now,

∵ If the simple Interest is $630, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃₀ years

∴ If the simple Interest is $5040, then the time = ¹/₆₃₀ × 5040 years

= ^{1 × 5040}/₆₃₀ years

= ⁵⁰⁴⁰/₆₃₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.

(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?

(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(9) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.