Question

,000 for 3. Suppo e it i" now 10years later, and wait tobaya-rest at 6% i You pay 810 the rest monthly) (a) Find the monthly payment years required to amorti b) How much total will you pay in interest for this loan? 4. Now suppose that instead of buying a house, you decided to rent one for less (and spend the $10,000 on a luxury vacation). You can use the monthly savings to deposit $500 at the end of every month into an account that pays 6% interest (compounded monthly). How much will you have in this account after 30 years?

Answer 1

Solution

Q3

Back-up Theory

Monthly Instalment Determination

Let P be the loan amount, n = number of years of payment, r = interest percent per month (or i in decimal form, i.e., r = 10% => i = 0.1) and x = monthly instalment.

Then, x = P/D, where D = {(1 + i)¹²ⁿ – 1}/{i(1 + i)¹²ⁿ}

And total interest paid = 12nx - P

Now, to work out the solution,

Details of calculations

Price = 200000

Down payment = 10000

So, loan amount = 200000 – 10000 = 190000

Refer to Back-up Theory given above for understanding of the working.

P	190000
r	6
i	0.005
n	30
12n	360
F = (1 + i)^12n	6.022575
D = (F - 1)/(ixF)	166.7916
x = P/D	1139.146
Total Payment	410092.6
Total Interest	220092.6

Part (a)

Monthly payment = $1139.15 Answer 1

Part (b)

Total interest paid = $220092.6 Answer 2

Q4

Back-up Theory

If a sum, P, is invested every month (at the start of the month) for T years at an interest rate of r% per annum, compounded monthly, the amount at the end of T years is:

A = P(12 + i)[{(12 + i)/12}^12T - 1)]/i

Details of calculations

P	500
T	30
12T	360
r	0.06
i	0.005
F1 = 12 + i	12.005
F2 = F1/12	1.000417
F3 = F2^12T	1.161798
F4 = F3 - 1	0.161798
F5 = F1/i	2401
A =P(F5xF4)	194238.4

So, amount in the account after 30 years = $194238.4 Answer 3

DONE