Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 7% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 7% 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 × 7}

= ²³⁹⁴⁰⁰/₃₉₉₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 7% 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 = 7% of Principal

= 7% of $5700

= ⁷/₁₀₀ × 5700

= ^{7 × 5700}/₁₀₀

= ³⁹⁹⁰⁰/₁₀₀ = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₉ years

∴ If the simple Interest is $2394, then the time = ¹/₃₉₉ × 2394 years

= ^{1 × 2394}/₃₉₉ years

= ²³⁹⁴/₃₉₉ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(8) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.

(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?