Question

Mr. Pitkin bought a farm and promised to pay $6825 in 6 years with 7% simple interest and $10925 in 14 years with 10.75% simple interest. Later, Mr. Pitkin met with the lender requesting to pay $6875 at the end of 4 years and to make a final payment at the end of 11 years. Based on a simple interest rate of 17.5%, determine the amount required to settle the debt at the end of 11 years.
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Answer 1

Let's calculate the principal amount of the first term of payments.

For the 6,825 payment in 6 years:

Maturity value = Principal x (1+(rate x time))

6825 = Principal x (1+(0.07 x 6))

6825 = 1.42 Principal

Principal = 6825 / 1.42

Principal = 4,806.33803

for the 10925 payment in 14 years:

Maturity value = Principal x (1+(rate x time))

10925 = Principal x (1+(0.1075 x 14))

10925 = 2.505 Principal

Principal = 10925 / 2.505

Principal = 4361.27745

Total amount borrowed = 4806.33803 + 4631.27745= 9167.61548

Now, calculate the principal amount of the second term:

For the 6,875 payment in 4 years:

Maturity value = Principal x (1+(rate x time))

6875 = Principal x (1+(0.175 x 4))

6875 = 1.7 Principal

Principal = 6875/ 1.7

Principal = 4044.11765

So, the principal amount of the second payment is = 9167.61548 – 4044.11765 = 5123.49783

We will calculate the maturity value of the second payment.

Maturity value = Principal x (1+(rate x time))

Maturity value = 5123.49783 x (1+(0.175 x 11))

Maturity value = 14986.2312

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