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

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

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+(r/2)/(100))^(2t)`

`=3000(1+(8/2)/(100))^(20)`

`=3000(1+(4)/(100))^(20)`

`=3000(1+0.04)^(20)`

`3000* (1.04)^(20)`

`=3000* 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.