A loan of $10,000 has an annual interest rate of 8%, compounded quarte

Question

A loan of $10,000 has an annual interest rate of 8%, compounded quarterly. What will be the total due (principal + interest) if no payment is made for 12 months?

(A) $800
(B) $824
(C) $10,800
(D) $10,824
(E) $11,600

lucasd14 · Accepted Answer

Correct procedure would be to calculate the Compounded Interest formula  . But we can save some time estimating and then comparing with the answer choices.

Let's consider 4 times the simple interest of 8%/4 (four quarters annually) * 10,000. That would be 200 * 4 = 800. Now we know that still is missing the compounded (the interest of the accumulative interest), so it must be something a bit greater than 800.  Only possible answer, D .

rsrighosh · Answer

is there any easier way to calculate  1.02^4

vaibhav1221 · Answer

Amount =  10000(1 + \frac{8}{400})^4 
=  \frac{(10000*51*51*51*51)}{(50*50*50*50)} 
=  \frac{(51*51*51*51)}{(5*5*5*5)} 
 \frac{51}{5}  =  10.2 
So,  (51*51*51*51)/(5*5*5*5)  =  (10.2)^4 = (10.2)^2*(10.2)^2

102*102 = 102*100 + 102*2 = 10200 + 204 = 10404 
So,  10.2*10.2 = 104.04

Now,  104*104 = 104*100 + 104*4 = 10400 + 416 = 10816 
So,  104.04*104.04  is slightly greater than  10816

Hence, the answer is D,  $10,824 .

Adarsh_24 · Answer

Using binomial expansion 
1.02^4 = (1+ 2/100)^4
=4c0 * 1^4* (2/100)^0
+4c1 * 1^3* (2/100)^1
+4c2 * 1^2* (2/100)^2
+4c3 * 1^1* (2/100)^3
+4c3 * 1^0* (2/100)^4

last two terms can be ignored as high powers of small numbers. So negligible.
rest will give 1+.08+.0024=1.0824

We could also approximate to 1+nx=1.08. Answer will be slightly higher than this.

sarthak1701 · Answer

Right off the bat you can reject A and B because the principal is not included. Next, you can reject 10,800 (C) as well because that'll be due if there is no compounding. The next 2 choices are spread apart, first quarter's interest is 200, next quarter's interest is 204, next quarter's interest is close to 208. It is clear that the due amount cannot exceed 11000 which leaves us only with Option D.

Aboyhasnoname · Answer

Rule..2% Compounded 4 times is always greater than 8% compounded once.....
Succesive Interest is always more than Flat interest... 
Answer Should be very Slights more than 10,800... 10,824....is the right option D

DonBosco7 · Answer

Finally after putting in the values in formula and factoring, it comes out to be

51x51x51x51/25x25

Now try multiplying only 50x50 = 2500
another 50x50 = 2500

2500 x 2500 = 6250000

divide this by 25x25 = 625

which comes out to be 10,000

but since we took 50 instead of 51 initially, the answer has to be little more than 10,000 
hence option D

A loan of $10,000 has an annual interest rate of 8%, compounded quarte

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A loan of $10,000 has an annual interest rate of 8%, compounded quarte

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