Lance Jackson deposited $5,000 at Basil Bank at 9% interest compounded daily. What is Lance's investment at the end of 4 years?
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compounded daily for 4 years = 365 x 4 = 1460 days.
[(0.09/365) + 1]^1460 x 5000 = ??
I get close to $7160 but that isn't exact. You need to go through the math.
To calculate Lance's investment at the end of 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $5,000
r = 9% = 0.09 (as a decimal)
n = 365 (daily compounding)
t = 4 years
Let's substitute these values into the formula and calculate the final amount:
A = $5,000(1 + 0.09/365)^(365*4)
Simplifying the exponent:
A = $5,000(1 + 0.000246575)^(1,460)
Calculating the exponent:
A = $5,000(1.000246575)^(1,460)
A ≈ $5,000(1.365972298)
A ≈ $6,829.86
Therefore, Lance's investment at the end of 4 years will be approximately $6,829.86.
To calculate Lance Jackson's investment at the end of 4 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $5,000
r = 9% = 0.09 (as a decimal)
n = 365 (compounded daily)
t = 4 years
Now, substitute these values into the formula:
A = $5,000(1 + 0.09/365)^(365*4)
To solve this equation, we can use a calculator or a spreadsheet software:
A = $5,000(1 + 0.000246)^1460
= $5,000(1.000246)^1460
≈ $5,000(1.4265)
Therefore, Lance Jackson's investment at the end of 4 years would be approximately $7,132.50.