David invested $3200 under a compound interest of 16% per annum in JAKE Investment Bank. If the interest rate was compounded half-yearly, then find the amount received by him after a year. Ops: A. $4230.8 B. $3214.5 C. $4370.4 D. $3732.48
Question
David invested 4230.8 B. 4370.4 D. $3732.48
Solution
To solve this problem, we need to use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
Given in the problem: P = $3200 r = 16% or 0.16 (in decimal) n = 2 (since the interest is compounded half-yearly) t = 1 year
Substituting these values into the formula:
A = 3200 (1 + 0.16/2)^(2*1) A = 3200 (1 + 0.08)^2 A = 3200 (1.08)^2 A = 3200 * 1.1664 A = $3732.48
So, the amount received by David after a year would be 3732.48.
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