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Finding the Interest Rate: Concept Connection Example 6-3 (page 237) 18. What interest rates are implied by the following lending arrangements?a. You borrow $500 and repay $555 in one year.b. You lend $1,850 and are repaid $2,078.66 in two years.c. You lend $750 and are repaid $1,114.46 in five years with quarterly compounding.d. You borrow $12,500 and repay $21,364.24 in three years under monthly compounding. (Note. In parts c and d, be sure to give your answer as the annual nominal rate.)Lasher, William R.. Practical Financial Management (Page 276). South-Western College Pub. Kindle Edition.

Question

Finding the Interest Rate: Concept Connection Example 6-3 (page 237) 18. What interest rates are implied by the following lending arrangements?

a. You borrow $500 and repay $555 in one year.

b. You lend $1,850 and are repaid $2,078.66 in two years.

c. You lend $750 and are repaid $1,114.46 in five years with quarterly compounding.

d. You borrow $12,500 and repay $21,364.24 in three years under monthly compounding. (Note. In parts c and d, be sure to give your answer as the annual nominal rate.)

Lasher, William R.. Practical Financial Management (Page 276). South-Western College Pub. Kindle Edition.

check_circleAnswer
Step 1

Interest rate:

An interest rate is a percentage on the principal amount at which a lender gives money to a borrower and it’s an excess amount on the principal amount. It is generally represented as an annual rate.     

 

Compounding Interest:          

It is the method for computing interest at the initial amount of principal which includes the previous period’s accumulated interest. It can be compounded annually, half-yearly, quarterly and daily. The rate of compounding interest depends on the frequency of compounding.

 

Formula for the calculation of Amount (A) using Compounded Interest:

Amount (A) = Principal Amount (P) * (1 + rate of interest (r) / Number of times compounded (n))n*time period

Step 2

(a)

Given,

Loan/Principal Amount (P) = $500

Repay Amount (A) = $555

Time in years (t) = 1

Type of compounding interest = Annually

 

Calculation of Interest rate:

Repay Amount (A) Loan/Principal Amount (P) * (1 Interest rate
()
fime
()
$555 $500 * (1 +Interest rate
$555 $5001 + Interest rate (r)
1.11 1Interest rate
(r)
1.11 1 Interest rate (r)
-
0.11 or 11% = Interest rate
(t)
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Repay Amount (A) Loan/Principal Amount (P) * (1 Interest rate () fime () $555 $500 * (1 +Interest rate $555 $5001 + Interest rate (r) 1.11 1Interest rate (r) 1.11 1 Interest rate (r) - 0.11 or 11% = Interest rate (t)

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Step 3

(b)

Given,

Lend/Principal Amount (P) = $1,850

Repaid Amount (A) = $2,078.66

Time in years (t) = 2

Type of c...

(1)t
Repaid Amount (A) Lend/Principal Amount (P) * (1 + Interest rate
fime
$2,078.66 $1,850 * (1 + Interest rate
())
$2,078.66 $1,850 (1Interest rate
(t)
()
(1Interest rate
1.1236
(1.1236)12 1 +Interest rate
()
1.06 1Interest rate
(r)
1.06 1
Interest rate (r)
0.06 or 6%
Interest rate (r)
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Image Transcriptionclose

(1)t Repaid Amount (A) Lend/Principal Amount (P) * (1 + Interest rate fime $2,078.66 $1,850 * (1 + Interest rate ()) $2,078.66 $1,850 (1Interest rate (t) () (1Interest rate 1.1236 (1.1236)12 1 +Interest rate () 1.06 1Interest rate (r) 1.06 1 Interest rate (r) 0.06 or 6% Interest rate (r)

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