Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9348

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 = $9348 – $5700 = $3648

Thus, Simple Interest = $3648

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 × 3648}/_{5700 × 8}

= ³⁶⁴⁸⁰⁰/₄₅₆₀₀

= 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) = $5700

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3648 (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 = 8% of Principal

= 8% of $5700

= ⁸/₁₀₀ × 5700

= ^{8 × 5700}/₁₀₀

= ⁴⁵⁶⁰⁰/₁₀₀ = 456

Thus, simple Interest for 1 year = $456

Now,

∵ If the simple Interest is $456, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₆ years

∴ If the simple Interest is $3648, then the time = ¹/₄₅₆ × 3648 years

= ^{1 × 3648}/₄₅₆ years

= ³⁶⁴⁸/₄₅₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(4) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.

(9) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.