Lynne invested $35,000 into an account earning 4% annual interest compounded quarterly. She makes no other deposits into the account and does not withdraw any money.
What is the balance of Lynne's account in 5 years?
$37,153.21
$39,438.88
$42,706.65 <my choice
$56,295.30
P' = P*(1+r/n)^{nt}
P' = 35000*(1+0,04/4)^{4*5}
P' = 35000*(1+0,01)^{20}
P' = 35000*(1,01)^{20}
P' = 35000*(1.22019003995...)
P' = 42,706.65
Correct!
To calculate the balance of Lynne's account in 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = $35,000
r = 4% = 0.04 (as a decimal)
n = 4 (compounded quarterly)
t = 5 years
Using the formula, we can calculate the balance of Lynne's account after 5 years:
A = 35,000(1 + 0.04/4)^(4*5)
A = 35,000(1 + 0.01)^(20)
A = 35,000(1.01)^(20)
A ≈ 35,000(1.2214)
A ≈ $42,749.89
Therefore, the correct answer is:
$42,706.65.
To find the balance of Lynne's account in 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance of the account
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $35,000
r = 4% or 0.04 (as a decimal)
n = 4 (compounded quarterly)
t = 5 years
Plugging these values into the formula, we can calculate the future balance:
A = $35,000(1 + 0.04/4)^(4*5)
A = $35,000(1 + 0.01)^(20)
A = $35,000(1.01)^20
A ≈ $35,000(1.2214)
A ≈ $42,749.06
So, based on the calculations, the balance of Lynne's account in 5 years would be approximately $42,749.06.
Among the given options, $42,706.65 is the closest value.