Problem Solving

Vincen wrote: ↑

Tue Jun 30, 2020 7:18 am

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?

(A) $10,100
(8) $10,101
(e) $10,200
(D) $10,201
(E) $10,400

[spoiler]OA=D[/spoiler]

Source: Official Guide

When the number of "compounding" periods is only 2 or 3, we can just calculate the interest for each period.
4% annual interest, compounded quarterly, means that for each quarter year (3 months), we are adding an interest of 1% to the amount in the bank. We can practically do this in our head.

Initial deposit = $10,000
Interest after 3 months = 1% of $10,000 = $100
Total after 3 months = $10,000 + $100 = $10,100

From here, the NEXT 3 months will yield an additional 1%
So, the interest for the next 3 months = 1% of $10,100 = $101
Total after 6 months = $10,100 + 101 = $10,201 = D

Cheers,
Brent

Vincen wrote: ↑

Tue Jun 30, 2020 7:18 am

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?

(A) $10,100
(8) $10,101
(e) $10,200
(D) $10,201
(E) $10,400

[spoiler]OA=D[/spoiler]

Source: Official Guide

Solution:

Since the account compounds quarterly, John earns 0.04/4 = 0.01, or 1 percent interest each quarter.

After Q1, he earns 10,000 x 0.01 = 100 dollars interest, and thus he has a total of 10,000 + 100 = 10,100 dollars in the account after the first quarter (or the first 3 months).

After Q2, John earns another 10,100 x 0.01 = 101 dollars interest.

So, after 6 months, the total amount of money in John’s account is 10,100 + 101 = 10,201 dollars.

Alternate Solution:

We can use the compound interest formula A = P[(1 + (r/n)]^(nt), with P = 10,000, r = 0.04, n = 4, and t = 0.5. Thus, we have P = 10,000[1+(0.04/4)]^2 = 10,000(1.01)^2 = 10,201.

Answer: D