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 $10921 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) = 7% per annum

Amount (A) = $10921

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 = $10921 – $6700 = $4221

Thus, Simple Interest = $4221

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 × 4221}/_{6700 × 7}

= ⁴²²¹⁰⁰/₄₆₉₀₀

= 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) = 7% per annum

Simple Interest = $4221 (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 $4221, then the time = ¹/₄₆₉ × 4221 years

= ^{1 × 4221}/₄₆₉ years

= ⁴²²¹/₄₆₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(2) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.

(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?

(9) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?