Use the compound interest formulas A = Pert and A = P(1 + 𝑟/n)^nt to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work.
continuous
A = P e^rt
A = 11,000 e^(.065 *10)
A = 11,000 * 1.9155
semiannual
20 periods at .0315 per period (6.3/2)
1.0315^20 = 1.859
A = 11,000 * 1.859 which is less :(
lol thank you so much again :)
You are welcome.
To determine which investment yields the greater return, we can use the compound interest formulas A = Pert and A = P(1 + 𝑟/n)^nt.
1. For the investment with 6.25% compounded continuously:
The formula is A = Pert, where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
t = the time in years
e = the mathematical constant approximately equal to 2.71828 (used in continuous compounding)
Plugging in the values:
P = $11,000
r = 6.25% = 0.0625 (in decimal form)
t = 10 years
A = Pert = 11000 * e^(0.0625*10)
Use a calculator to calculate e^(0.0625*10), then multiply the result by $11,000 to find the future value.
2. For the investment with 6.3% compounded semiannually:
The formula is A = P(1 + 𝑟/n)^nt, where:
n = the number of compounding periods per year
Plugging in the values:
P = $11,000
r = 6.3% = 0.063 (in decimal form)
t = 10 years
n = 2 (semiannual compounding)
A = P(1 + 𝑟/n)^nt = 11000(1 + 0.063/2)^(2*10)
Use a calculator to calculate (1 + 0.063/2)^(2*10), then multiply the result by $11,000 to find the future value.
Compare the two future values obtained from each formula to determine which investment yields the greater return over 10 years. The investment with the larger future value will have a greater return.