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

Explanation:

`A = P\bigg(1+(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+(0.0804)/(365)\bigg)^(365* 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+(0.081)/(4)\bigg)^(4* 10)\\\\.\ =\$ 6,689.37`

Option A results in the greater amount of money.