Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12127

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 = $12127 – $6700 = $5427

Thus, Simple Interest = $5427

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 × 5427}/_{6700 × 9}

= ⁵⁴²⁷⁰⁰/₆₀₃₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 9% per annum

Simple Interest = $5427 (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 = 9% of Principal

= 9% of $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $5427, then the time = ¹/₆₀₃ × 5427 years

= ^{1 × 5427}/₆₀₃ years

= ⁵⁴²⁷/₆₀₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(2) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(4) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(6) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.