ACT Math · Exponential and logarithmic functions

$1,000 is invested at 6% annual interest, compounded annually. Which value is closest to the balance after 2 years?

$1,000 is invested at 6% annual interest, compounded annually. Which value is closest to the balance after 2 years?

Answer and explanation

Answer: C: $1,124

With annual compounding, each year's interest is added before the next year's is computed: 1000(1.06)2=1000(1.1236)=1123.601000(1.06)^2=1000(1.1236)=1123.60, which is closest to $1,124, choice C. Year 1 gives $1,060, and year 2 earns 6\% on $1,060, which is $63.60. Choice B ($1,120) uses simple interest, 1000+2(60)1000+2(60), and misses the $3.60 earned on the first year's interest. Choice A ($1,060) is the balance after only one year. Choice D ($1,360) uses 6%6\% per year for 66 years or another wrong exponent, far too much.

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