Question

Brian wants to have $7000 in the bank in 10 years. He deposits $3000 today at 8% interest compounded semiannually,After keeping the money in the bank for 10 years, how much more money will he need to add to his account to reach the desired balance of  $7000? a. $341.08 c. $1600 b. $426.63 d. $0

Answer 1

Total = Principal * ((1 + rate/n)^(n*years)
Total = 3,000 * (1.04)^20
Total = 3,000 * 2.191123143 =  6,573.37
So, he will have to add (7,000 - 6,573.37) =
$ 426.63
answer is b
Here's a calculator to check your work http://www.1728.org/compint.htm

Answer 2

Answer: He need to add approximately $ 426.63 to his account to reach the desired balance of  $7000.

Step-by-step explanation:

Here, the principal amount, P = $ 3000,

Semiannual rate of interest, r = 8 %

Time, t = 10 years,

Hence, the amount after 10 years, which is compounded with the semiannual rate of 8% for 10 years,

$A=P(1+\frac{r/2}{100})^{2t}$

$=3000(1+\frac{8/2}{100})^{20}$

$=3000(1+\frac{4}{100})^{20}$

$=3000(1+0.04)^{20}$

$3000\times (1.04)^{20}$

$=3000\times 2.19112314303=\ 6573.3694291$

Thus, the amount, need to add in the balance to reach the amount of $ 7000 = 7000 - 6573.3694291 = 426.6305709 ≈ $ 426.63

⇒ He need to add approximately $ 426.63 to his account to reach the desired balance of  $7000.

⇒ Option B is correct.