Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8094

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 = $8094 – $5700 = $2394

Thus, Simple Interest = $2394

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 × 2394}/_{5700 × 6}

= ²³⁹⁴⁰⁰/₃₄₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 6% per annum

Simple Interest = $2394 (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 $5700

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = 342

Thus, simple Interest for 1 year = $342

Now,

∵ If the simple Interest is $342, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₂ years

∴ If the simple Interest is $2394, then the time = ¹/₃₄₂ × 2394 years

= ^{1 × 2394}/₃₄₂ years

= ²³⁹⁴/₃₄₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.