What is the ending balance in an account that opebs with $7000, earns 7.5% interest compound quarterly, and is held for 20 years.
Pt = Po(1+r)^n.
r=(7.5%/4) / 100%=0.01875 = Quarterly % rate expressed as a decimal.
n = 4Comp./yr * 20yrs = 80 Compounding
periods.
Pt = 7000(1.01875)^80 = $30,939.11
To calculate the ending balance in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the ending balance
P = the initial principal (amount at the start)
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 = $7000
r = 7.5% (0.075 as a decimal)
n = 4 (quarterly compounding)
t = 20 years
Plugging in these values into the formula, we have:
A = $7000(1 + 0.075/4)^(4*20)
Calculating this expression step by step:
1. r/n = 0.075/4 = 0.01875
2. 1 + r/n = 1 + 0.01875 = 1.01875
3. (1 + r/n)^(n*t) = (1.01875)^(4*20) ≈ 3.478
4. A = $7000 * 3.478 ≈ $24346.04
Therefore, the ending balance in the account after 20 years would be approximately $24,346.04.
To calculate the ending balance of an account with compound interest, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the initial amount (or principal), which is $7000 in this case
r = the interest rate per period, which is 7.5% or 0.075 in decimal
n = the number of compounding periods per year, which is 4 (quarterly)
t = the number of years the money is invested for, which is 20 years
Plugging in these values into the formula, we can calculate the ending balance:
A = 7000(1 + 0.075/4)^(4*20)
A ≈ 7000(1 + 0.01875)^(80)
A ≈ 7000(1.01875)^(80)
Calculating this using a calculator or a spreadsheet program, the approximate ending balance is $25,676.41.
Therefore, the ending balance in the account after 20 years would be approximately $25,676.41.