Bathsheba is saving up for the down payment on a farm. She invests $30000 at 5.2% interest, compounded quarterly, for 4 years. To the nearest tenth of a percent, Bathsheba's rate of return will be ____%.
P = Po(1+r)n
r = (5.2%/4)/100% = 0.013 = Quarterly %
rate expressed as a decimal.
n = 4comp/yr * 4yrs = 16 Compounding
periods.
P = 30,000(1.013)^16 = $36,886.92
((36886.92-30000)/30000) * 100% = 23%
Return rate.
Thank you!
To calculate Bathsheba's rate of return, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (including principal and interest)
P = the principal amount (the initial investment)
r = interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, Bathsheba invests $30,000 at an interest rate of 5.2% (or 0.052 as a decimal), compounded quarterly (so n = 4), for 4 years.
Plugging these values into the formula, we have:
A = 30000(1 + 0.052/4)^(4*4)
A ≈ 30000(1 + 0.013)^16
A ≈ 30000(1.013)^16
Using a calculator, we can evaluate (1.013)^16 ≈ 1.21905.
A ≈ 30000 * 1.21905
A ≈ 36571.5
The final amount, including principal and interest, is approximately $36,571.50.
To calculate Bathsheba's rate of return (or rate of interest), we need to find the difference between the final amount and the initial investment, divided by the initial investment:
Rate of return = (A - P) / P * 100%
Rate of return ≈ (36571.5 - 30000) / 30000 * 100%
Rate of return ≈ 0.21905 * 100%
Rate of return ≈ 21.9%
Therefore, Bathsheba's rate of return to the nearest tenth of a percent is approximately 21.9%.