Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9943

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 = $9943 – $6100 = $3843

Thus, Simple Interest = $3843

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 × 3843}/_{6100 × 7}

= ³⁸⁴³⁰⁰/₄₂₇₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6100

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

Simple Interest = $3843 (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 $6100

= ⁷/₁₀₀ × 6100

= ^{7 × 6100}/₁₀₀

= ⁴²⁷⁰⁰/₁₀₀ = 427

Thus, simple Interest for 1 year = $427

Now,

∵ If the simple Interest is $427, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₇ years

∴ If the simple Interest is $3843, then the time = ¹/₄₂₇ × 3843 years

= ^{1 × 3843}/₄₂₇ years

= ³⁸⁴³/₄₂₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?

(7) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(9) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?