If P = 1,000, R = 5% p.a, n = 4; What is Amount and C.I. isa.1,215.50, 215.50b.1,125, 125c.2,115, 115d.2,215, 215
Question
If P = 1,000, R = 5% p.a, n = 4; What is Amount and C.I.
a. 1,215.50, 215.50
b. 1,125, 125
c. 2,115, 115
d. 2,215, 215
Solution
The question is asking for the total amount and compound interest (C.I.) given the principal (P), rate of interest (R), and number of years (n). The formula for compound interest is A = P(1 + R/n)^(nt), where A is the amount of money accumulated after n years, including interest.
Given: P = 1,000 R = 5% per annum = 0.05 (in decimal form) n = 4 years
Step 1: Convert the rate from percentage to decimal form. R = 5/100 = 0.05
Step 2: Substitute the values into the formula. A = 1000(1 + 0.05/1)^(1*4) A = 1000(1 + 0.05)^4 A = 1000(1.05)^4 A = 1000 * 1.21550625 A = 1215.50625
The total amount after 4 years will be approximately 1215.51 (when rounded to the nearest penny).
The compound interest (C.I.) is the total amount minus the principal. C.I. = A - P C.I. = 1215.51 - 1000 C.I. = 215.51
So, the answer is a. 1,215.50, 215.50.
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