Question

Sebastian deposited money into an account in which interest is compounded monthly at a rate of 2.3% How much did he deposit if the total amount in his account after 5 years was $2123.47, and he made no other deposits or withdrawals. A.$1879. B.$1893. C.$2055. D.$2075.

Answer 1

Answer: B. $1893

Step-by-step explanation:

Given: The rate of interest =2.3%

In decimal, the rate of interest  $r=0.023$

The amount after 5 years = $2127

Let P be the initial invested  amount.

The The formula for annual compound interest (compounded monthly)is given by:-

$A=P(1+\frac{r}{12})6^{12t}\\\\\Rightarrow\ 2123.47=P(1+\frac{0.023}{12})^{12\times5}\\\\\Rightarrow\ 2123.47=P(1.00191666666667)^{60}\\\\\Rightarrow\ 2123.47=P( 1.12174996232)\\\\\Rightarrow\ P=\frac{2123.47}{1.12174996232}\\\\\Rightarrow\ P=1892.99761206\approx1893$

Therefore, the initial deposit = $1893

Answer 2

Use the attached formula,

Principal = 2,123.47 / (1+ (.023/12))^12*5
Principal = 2,123.47 / 1.0019166667 ^ 60
Principal = 2,123.47 / 1.1217499623
Principal = 1892.9976120547
Principal = 1893.00 (rounded)

answer is B