Question

when the rate is compounded half yearly, what will be the change comes in Time​

Answer 1

Answer:

If the rate of interest is annual and the interest is compounded half-yearly (i.e., 6 months or, 2 times in a year) then the number of years (n) is doubled (i.e., made 2n) and the rate of annual interest (r) is halved (i.e., made r2).

Answer 2

Answer:

Here, the interest is compounded half-yearly. So,

Principal (P) = $ 4,000

Number of years (n) = 11212 × 2 = 3232 × 2 = 3

Rate of interest compounded half-yearly (r) = 102102% = 5%

Now, A = P (1 + r100r100)nn

⟹ A = $ 4,000(1 + 51005100)33

⟹ A = $ 4,000(1 + 120120)33

⟹ A = $ 4,000 × (21202120)33

⟹ A = $ 4,000 × 9261800092618000

⟹ A = $ 4,630.50 and

Compound interest = Amount - Principal

                          = $ 4,630.50 - $ 4,000

                          = $ 630.50

Therefore, the amount is $ 4,630.50 and the compound interest is $ 630.50