Answer:
Correct answer: 1) AV = 12,290 $, 2) AV = 12,310 $, 3) AV = 12,330 $,
4) AV = 12,337 $
Step-by-step explanation:
Given:
I = 10,000$
n = 3 years
p = 7% = 0.07
Accumulated value of an investment is calculated with next formula:
AV = I · (1 + (p/a))ᵃⁿ where is:
AV - accumulated value
I - investment
p - interest
a - number of calculation parts during one year as the accounting period
n - number of years as the accounting period
1) money is compounded semiannually
a = 2 and a · n = 2 · 3 = 6
AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/2))⁶ = 10,000 · 1.229 = 12,290 $
AV = 12,290 $
2) money is compounded quarterly
a = 4 and a · n = 4 · 3 = 12
AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/4))¹² = 10,000 · 1.231 = 12,310 $
AV = 12,310 $
3) money is compounded monthly
a = 12 and a · n = 12 · 3 = 36
AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/12))³⁶ = 10,000 · 1.233 = 12,330 $
AV = 12,330 $
4) money is compounded continuously
Accumulated value of an investment continuously compounded is calculated with next formula:
AV = I · eⁿᵇ where is:
n - number of years as the accounting period
b = p = 7% = 0.07
n · b = 3 · 0.07 = 0.21
AV = 10,000 e⁰²¹ = 10,000 2.7183⁰²¹ = 10,000 1.2337 = 12,337 $
AV = 12,337 $
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