Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8320

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 = $8320 – $5200 = $3120

Thus, Simple Interest = $3120

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 × 3120}/_{5200 × 10}

= ³¹²⁰⁰⁰/₅₂₀₀₀

= 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) = $5200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3120 (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 = 10% of Principal

= 10% of $5200

= ¹⁰/₁₀₀ × 5200

= ^{10 × 5200}/₁₀₀

= ⁵²⁰⁰⁰/₁₀₀ = 520

Thus, simple Interest for 1 year = $520

Now,

∵ If the simple Interest is $520, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₀ years

∴ If the simple Interest is $3120, then the time = ¹/₅₂₀ × 3120 years

= ^{1 × 3120}/₅₂₀ years

= ³¹²⁰/₅₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?

(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

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

(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.