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 $9690 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9690

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 = $9690 – $5700 = $3990

Thus, Simple Interest = $3990

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 × 3990}/_{5700 × 7}

= ³⁹⁹⁰⁰⁰/₃₉₉₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3990 (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 $3990, then the time = ¹/₃₉₉ × 3990 years

= ^{1 × 3990}/₃₉₉ years

= ³⁹⁹⁰/₃₉₉ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

(5) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(6) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.