Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6314

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 = $6314 – $4100 = $2214

Thus, Simple Interest = $2214

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 × 2214}/_{4100 × 6}

= ²²¹⁴⁰⁰/₂₄₆₀₀

= 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) = $4100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2214 (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 = 6% of Principal

= 6% of $4100

= ⁶/₁₀₀ × 4100

= ^{6 × 4100}/₁₀₀

= ²⁴⁶⁰⁰/₁₀₀ = 246

Thus, simple Interest for 1 year = $246

Now,

∵ If the simple Interest is $246, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₆ years

∴ If the simple Interest is $2214, then the time = ¹/₂₄₆ × 2214 years

= ^{1 × 2214}/₂₄₆ years

= ²²¹⁴/₂₄₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.

(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(6) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?