Question

You wish to purchase a new watch for your mother, which will cost $16,300. You have arranged a loan that only covers part of the purchase price and intend to finance the rest of the purchase with money from your own savings. The interest rate on the loan is 6.5% p.a. compounded semi-annually. The loan requires payments of $250 per month for 3 years. How much of your own savings must you use?

Group of answer choices

$8,132.66

$8,247.18

$8,167.34

$8,058.62

$8,235.72

Kiran is thinking about purchasing a birthday gift for his girlfriend. Instead of a handbag or jewellery, he will buy a financial asset for her. He thinks this is a wonderful gift because this asset will payout a certain annual cash flow from her 26^thbirthday until her 35^th birthday. The cash flow will be $5,000 on her 26^th birthday and this will grow at a rate of 3% each year. How much would Kiran have to pay on his girlfriend's 25th birthday for this asset if he paid the fair value assuming a constant interest rate of 5% p.a. compounding annually?

Group of answer choices

$45,570.39

None of the options

$42,189.55

$40,036.87

$43,737.98

Answer 1

Here given,

Interest rate on Loan = 6.5% p.a
If it is compounded semi-annually, we get interest rate as [(1 +0.065/2)^2]-1 = 6.6056% compounded semi-annually

Hence, presenting it in amortization table

Annual Interest rate	6.6056%
Years	3
Payments per year	12
Loan Amount ($)	8132.66
Payment Number	Payment	Interest	Principal	Balance
1	250.00	44.77	204.88	7,927.78
2	250.00	43.64	206.01	7,721.77
3	250.00	42.51	207.14	7,514.63
34	250.00	4.08	245.57	495.21
35	250.00	2.73	246.92	248.28
36	250.00	1.37	248.28	0.00

Hence, out of $ 16,300
$ 8132.66 is the loan amount.
Therefore, I should use $16,300- $8,132.66 = $ 8,167.34 from my savings.