Question

Itzak Perlman Corporation needs $15,000,000 in ten years to be able to retire bonds that will be maturing at that time. What amount must Perlman deposit into a bond sinking fund at the end of each year if the fund is expected to earn interest at a rate of 8% per year?

2. Igor Stravinsky is retiring today. His employer has given the option of taking a lump sum payout of his pension or receiving quarterly annuity payments for the next seven years. He could receive $950,000 today or receive $45,000 every three months for seven years, with the first payment received today. If money is worth 2% per quarter, compounded quarterly, which option would you recommend to Stravinsky?

3. Tchaikovsky Company purchased a custom-made grand piano on December 31, 2002. The purchase agreement stipulated that Tchaikovsky should pay $25,000 at the time of the purchase and $5,000 every six months for the next four years. The first of eight $5,000 payments would occur six months from today. Assuming an appropriate interest rate of 4% per year, what is the cost of the piano?

Answer 1

Solution to QUESTION-1

The amount to be deposited by Perlman into the bond sinking fund at the end of each year

Here, we have Future Value = $15,000,000

Annual interest rate (r) = 8.00% per year

Number of periods (n) = 10 Years

Annual deposit payment (P) = ?

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

$15,000,00 = P x [{(1 + 0.08)¹⁰ - 1} / 0.08]

$15,000,00 = P x [(2.158924997 – 1) / 0.08]

$15,000,00 = P x [1.158924997 / 0.08]

$15,000,00 = P x 14.48656247

P = $15,000,000 / 14.48656247

P = $1,035,442.33

“Hence, the amount to be deposited by Perlman into the bond sinking fund at the end of each year will be $1,035,442.33”