Question

The borrower in a $238,000 loan makes interest payments at the end of each six months for eight years. These are computed using an annual effective discount rate of 6.5%. Each time he makes an interest payment, the borrower also makes a deposit into a sinking fund earning a nominal interest rate of 4.2% convertible monthly. The amount of each sinking fund deposit is D in the first three years and 2D in the remaining five years, and the sinking fund balance at the end of the eight years is equal to the loan amount. Find D.

Answer 1

Answer:

D = 7980.55

Explanation:

Since the borrower pays in 6 months wich is half a year, we calculate the semi-annual rate = $\frac{Annual rate of intrest}{Number of months}$

= $\frac{0.042}{12}$

= 0.0035 = 0.35%

The effective semi-annual rate is, [(0.0035)⁶- 1] = 0.02118461

$\frac{D[(1.02118461)^{16} - 1]}{1.02118461) - 1}$ + $\frac{D[(1.02118461)^{10} - 1]}{1.02118461) - 1}$ = 238000

$\frac{D(1.398518 - 1)}{0.02118461}$ + $\frac{D(1.233226 - 1)}{0.02118461}$ = 238000

0.631744D = 238000 * 0.02118461

0.631744D = 5041.937

Therefore D = 7980.55

Answer 2

SInking funds are the funds or the money that is kept aside by the company for paying off future debts or bonds. This amount cannot be sed for any other payments. This helps in balancing the financial economy of the entity.

The value of D is $7,980.55

Computation:

Given:

• Loan amount =$238,000
• Interest payment period =semi annual rate
• annual effective discount rate =6.5%
• nominal interst rate convertible monthly =4.2%

Computation of effective semi-annual interest rate:

$\text{Effective semi-annual interest rate}=(\dfrac{\text{Nominal Interest rate}}{\text{Number of month}})^\text{Payment period}-1\\\\=(\dfrac{0.042}{12})^6-1\\\\=(0.035)^6-1\\\\=0.02118\;\text{or}\;2.12\%$

The value of D will be computed based upon the total loan payment formula:

$\begin{aligned} \text{Loan}&=\dfrac{\text{D(1+i)}^\text{n}-1}{(1+\text{i}-1)}\\&+\dfrac{\text{2D(1+i)}^\text{n}-1}{(1+\text{i}-1)}\\\ 238,000&=\dfrac{\text{D}(1+0.02118)^{16}-1}{(1+0.02118)-1}+\dfrac{\text{2D}(1+0.02118)^{16}-1}{(1+0.02118)-1}\\\ 238,000\times0.02118&=0.63174\text{D}\\\text{D}&=\ 7,980.55\end{aligned}$

were,

D is sinking fund deposit

i is the effective interest rate

n is the number of payment period

To know more about sinking funds, refer to the link:

https://brainly.com/question/8500652