Please help me and show an understanding please, so I see how to figure them out.
Lee deposited $28,000 in an interest-bearing checking account that earns 3.5% interest compounded daily. Find the amount after 68 days.
a.$183.16
b.$28,180.46
c.$28,183.16
d.$180.46
On April 10th, Nicholas deposited $3,000 in a savings account paying 3.5% compounded daily. He deposited an additional $650 on April 20 and $1,200 on May 18. Find the compound amount on May 30.
a. $4,850
b. $4,873.31
c. $4,868.30
d. $48.30
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The first one, I got close to the answers, but its not any one of the choices. So please help. and the last one, I have no idea how to do it.
i = .035/365 = .00009589.. (I store this in my calculator memory so I don't lose any accuracy)
amount = 28000(1 + .00009589..)^68
= 28183.16
for the 2nd problem,
the 3000 earns interest for 20 + 30 or 50 days
the 650 for 10+30 or 40 days
then 1200 for 12 days
amount = 3000(1.00009589)^50 + 650(1.00009589)^40 + 1200(1.00009589)^12
= 4868.296 , not bad eh?
To find the amount after a certain number of days in an interest-bearing checking account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial deposit
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years
For the first question, we are given:
P = $28,000
r = 3.5% = 0.035 (as a decimal)
n = 365 (since it compounds daily)
t = 68 days
Plugging these values into the formula:
A = $28,000(1 + 0.035/365)^(365*68/365)
A = $28,000(1 + 0.00009589)^(68)
A ≈ $28,183.16
Thus, the answer is option c. $28,183.16.
For the second question, we need to find the compound amount on May 30th. Here, we have multiple deposits, so we can calculate the amount separately for each deposit and then add them up.
First deposit:
P₁ = $3,000
r = 3.5% = 0.035 (as a decimal)
n = 365 (daily compounding)
t₁ = 20 days (from April 10th to April 30th)
A₁ = $3,000(1 + 0.035/365)^(365*20/365)
A₁ = $3,000(1 + 0.00009589)^(20)
A₁ ≈ $3,048.51
Second deposit:
P₂ = $650
t₂ = 10 days (from April 20th to April 30th)
A₂ = $650(1 + 0.035/365)^(365*10/365)
A₂ = $650(1 + 0.00009589)^(10)
A₂ ≈ $656.72
Third deposit:
P₃ = $1,200
t₃ = 20 days (from May 18th to May 30th)
A₃ = $1,200(1 + 0.035/365)^(365*20/365)
A₃ = $1,200(1 + 0.00009589)^(20)
A₃ ≈ $1,216.08
The compound amount on May 30th is the sum of these amounts:
Total amount = A₁ + A₂ + A₃
Total amount ≈ $3,048.51 + $656.72 + $1,216.08
Total amount ≈ $4,921.31
Thus, the answer is not among the given options.
To find the amount after a given period of time in an interest-bearing checking account, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after time t
P = the principal (initial amount deposited)
r = annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the time in years
Now let's apply this formula to both problems:
1. Lee deposited $28,000 in an interest-bearing checking account that earns 3.5% interest compounded daily. We need to find the amount after 68 days.
P = $28,000
r = 3.5% = 0.035 (as a decimal)
n = 365 (since interest is compounded daily)
t = 68/365 ≈ 0.1863 (approximately 0.1863 years)
A = $28,000(1 + 0.035/365)^(365*0.1863)
≈ $28,000(1.00009575)^67.395
≈ $28,000(1.0643544874)
≈ $29,818.87
The amount after 68 days is approximately $29,818.87. Unfortunately, none of the provided answer choices match exactly. It's possible that there is a rounding issue with the answer choices, or a mistake in the problem itself.
2. Nicholas deposited $3,000 on April 10th, $650 on April 20th, and $1,200 on May 18th. We need to find the compound amount on May 30th.
To solve this problem, we need to calculate the amount separately for each deposit, and then add them together.
On April 10th:
P1 = $3,000
r = 3.5% = 0.035 (as a decimal)
n = 365 (since interest is compounded daily)
t1 = 20/365 ≈ 0.0548 (approximately 0.0548 years)
A1 = $3,000(1 + 0.035/365)^(365*0.0548)
≈ $3,000(1.00009575)^19.97
≈ $3,000(1.0666976765)
≈ $3,200.09
On April 20th:
P2 = $650
r = 3.5% = 0.035 (as a decimal)
n = 365 (since interest is compounded daily)
t2 = 10/365 ≈ 0.0274 (approximately 0.0274 years)
A2 = $650(1 + 0.035/365)^(365*0.0274)
≈ $650(1.00009575)^9.99
≈ $650(1.0288195986)
≈ $668.21
On May 18th:
P3 = $1,200
r = 3.5% = 0.035 (as a decimal)
n = 365 (since interest is compounded daily)
t3 = 12/365 ≈ 0.0329 (approximately 0.0329 years)
A3 = $1,200(1 + 0.035/365)^(365*0.0329)
≈ $1,200(1.00009575)^11.99
≈ $1,200(1.0393000411)
≈ $1,247.16
Adding the amounts together:
Compound Amount on May 30th = A1 + A2 + A3
= $3,200.09 + $668.21 + $1,247.16
≈ $5,115.46
The compound amount on May 30th is approximately $5,115.46. None of the provided answer choices match exactly, so there may be a rounding issue or mistake in the problem itself.