pf.5 compound interest - homework\nscore: 12.84/52 answered: 18/19\nquestion 18\nsuppose $13,000.00 is…

pf.5 compound interest - homework\nscore: 12.84/52 answered: 18/19\nquestion 18\nsuppose $13,000.00 is invested in an account for 15 years. calculate the total interest earned at the end of 15 years if the interest is:\n(a) 8% simple interest:\n(b) 8% compounded annually:\n(c) 8% compounded quarterly:\n(d) 8% compounded monthly:\nhint\nquestion help: video 1 video 2

pf.5 compound interest - homework\nscore: 12.84/52 answered: 18/19\nquestion 18\nsuppose $13,000.00 is invested in an account for 15 years. calculate the total interest earned at the end of 15 years if the interest is:\n(a) 8% simple interest:\n(b) 8% compounded annually:\n(c) 8% compounded quarterly:\n(d) 8% compounded monthly:\nhint\nquestion help: video 1 video 2

Answer

Explanation:

Step1: Simple Interest Formula

The formula for simple interest is (I = Prt), where (P=$13000), (r = 0.08), and (t = 15) years. [I=13000\times0.08\times15] [I = 13000\times1.2] [I=$15600]

Step2: Compound Interest Formula (Annual)

The compound - interest formula is (A=P(1 + r)^{t}), where (P = 13000), (r=0.08), (t = 15). [A = 13000\times(1 + 0.08)^{15}] [A=13000\times(1.08)^{15}] Using a calculator, ((1.08)^{15}\approx3.17215) [A=13000\times3.17215=$41237.95] Interest (I=A - P) [I=41237.95-13000=$28237.95]

Step3: Compound Interest Formula (Quarterly)

The compound - interest formula is (A = P\left(1+\frac{r}{n}\right)^{nt}), where (P = 13000), (r = 0.08), (n = 4) (quarterly compounding), (t = 15) [A=13000\left(1+\frac{0.08}{4}\right)^{4\times15}] [A=13000(1 + 0.02)^{60}] Using a calculator, ((1.02)^{60}\approx3.28103) [A=13000\times3.28103=$42653.39] Interest (I=A - P) [I=42653.39-13000=$29653.39]

Step4: Compound Interest Formula (Monthly)

The compound - interest formula is (A = P\left(1+\frac{r}{n}\right)^{nt}), where (P = 13000), (r = 0.08), (n = 12) (monthly compounding), (t = 15) [A=13000\left(1+\frac{0.08}{12}\right)^{12\times15}] [A=13000\left(1+\frac{0.08}{12}\right)^{180}] Using a calculator, (\left(1+\frac{0.08}{12}\right)^{180}\approx3.30459) [A=13000\times3.30459=$42959.67] Interest (I=A - P) [I=42959.67-13000=$29959.67]

Answer:

(a) ($15600) (b) ($28237.95) (c) ($29653.39) (d) ($29959.67)