Question

suppose that you have 3000$ to invest. which investment yields the greater return over a 10 year period: 8.04% compounded daily lf 8.1% compounded quarterly?

Answer 1

Answer:  Option A: 8.04% compounded daily

Step-by-step explanation:

$A = P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\qquad where\\\\\bullet A = \text{accrued amount (principal plus interest earned)}\\\bullet P = \text{principal (amount invested)}\\\bullet r = \text{rate (in decimal form)}\\\bullet n=\text{number of times compounded in one year}\\\bullet t=\text{time (number of years)}\\\\\\Option\ A:\\A = \text{unknown}\\P=3000\\r=8.04\%\rightarrow 0.0804\\n=\text{daily}\rightarrow 365\\t=10\\\\A=3000\bigg(1+\dfrac{0.0804}{365}\bigg)^{365\times 10}\\\\.\ =\ 6,702.79$

$Option\ B:\\A = \text{unknown}\\P=3000\\r=8.1\%\rightarrow 0.081\\n=\text{quarterly}\rightarrow 4\\t=10\\\\A=3000\bigg(1+\dfrac{0.081}{4}\bigg)^{4\times 10}\\\\.\ =\ 6,689.37$

Option A results in the greater amount of money.