6) Alberto invests $8,534 in a retirement
2 answers:
Answer:
It will take 17.2 years to reach account balance of $16826.03
Step-by-step explanation:
Given
Principal amount P = $ 8534
rate of interest r = 4% = 4/100 = 0.04
No of times interest is compounded, n = 12
Final amount A = $ 16826.03
To find: time in years, t = ?
We know that final amount of compound interest A is given by formula:
A = P
Substituting known values,
16826.03 = 8534 *
= 1.972
= 1.972
take log on both sides,
ln = ln (1.972)
12t * ln (1.0033) = ln (1.972) (since ln = n * ln x)
12t = 206.112
t = 17.2 years
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This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =
N(c₂) =
∴N(c₁c₂) =
∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =
N(c₂) =
∴N(c₁c₂) =
∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4