Question

Robin owes $4000 after 3 years and $4500 after 7 years. Robin is unable to meet her obligation after 3 years and by mutual agreement is allowed to pay off both notes with a single payment after 6 years. Find the size of Robin’s payment after 6 years if 8% quarterly is used in the settlement.

Dan borrows $1500.00 with 8% simple interest and repays this loan with a payment of $500.00 after 3 months, $500.00 after 7 months then a final payment at the end of one year to settle the debt. Find the size of Dan’s payment after one year using U.S. Rule.

Suppose I make a deposit of $6000.00 into a bank account earning 7% monthly today with the hopes of making an equal withdrawal each year for four years with the first coming exactly 8 years from now. Find the size of this equal annual withdrawal.

Answer 1

Answer :

(1)

Robin owes $4000 after 3 years and $4500 after 7 years

As Robin is unable to pay obligation after 3 years and will pay after 6 years

Thus, calculation obligation after 6 years :

Future amount = Amount*(1+r)^n

Where r = Interest rate = 8%/4 = 2%

n = no of years = (6year -3years)*4 = 12

Future amount = $4000*(1+0.02)^12

= $5072.97

So, obligation in 6th year = $5072.97

Now, Calculating the value of obligation to be paid in 7 years at 6th year

Present amount = Amount/(1+r)^n

Where r = Interest rate = 8%/4 = 2%

n = no of years = (7year - 6year)*4 = 4

Present amount = $4500/(1+0.02)^4

= $4157.30

Thus, final settlement of obligation in 6th year = $5072.97 + $4157.30

= 9230.27

(2).

Total borrowings = Present value of payments

$15,000 = $500*PVF(0.667%p.m,3 months) + $500 PVF(0.667%p.m, 7 months) + Balance

Balance = $15,000 - $490.13 - $477.27 = $14,032.61

Present value of payment after 1 year = $14,032.61

Paid amount*PVF(8%, 1 year) = $14,032.61

After 1 year paid amount = $14,032.61 / 0.9259 = $15,155.22

(3).

PV of deposit	$6,000.00
Years of deposit	8
Rate	7%
PV of deposit amount	$10,309.12
Year of withdrawal	4
Size of annual withdrawal	$3,043.54