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Tasha invests $5,000 annually at 6% and an additional $5,000 annually at 8%. Thomas invests $10,000 annually at 7%. Which statement accurately compares the two investments if interest is compounded annually?

Compound interest formula: mc020-1.jpg
t = years since initial deposit
n = number of times compunded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years
Each person will have exactly the same amount over time because each invested $10,000 at an average interest rate of 7%.
Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.
Thomas’s investment will yield more from the start because he has more money invested at the average percentage rate.
Tasha’s investment will be greater at first because she invested some at a higher rate, but Thomas’s investment will be greater over the long run.

Respuesta :

isyllus

Answer:

B is correct.

Step-by-step explanation:

Compound Interest Formula:

[tex]V(t)=P(1+\frac{r}{n})^{nt}[/tex]

Tasha invests in two ways

Case 1:

  • Principal P=$5,000
  • Rate of Interest r=0.06
  • Time t=t
  • n=1

[tex]V(t)=5000(1+0.06)^t[/tex]

[tex]V(t)=5000(1.06)^t[/tex]

Case 2:

  • Principal P=$5,000
  • Rate of Interest r=0.08
  • Time t=1
  • n=1

[tex]V(t)=5000(1+0.08)^t[/tex]

[tex]V(t)=5000(1.08)^t[/tex]

Total amount yield by Tasha = [tex]5000[(1.06)^t+(1.08)^t][/tex]

Thomas Investment

  • Principal P=$10,000
  • Rate r= 0.07
  • t=t
  • n=1

Total amount yield by Thomas = [tex]10000(1.07)^t[/tex]

Now we make table for Tasha and Thomas different value of t

    t                  Tasha                  Thomas

   1                  $10,700                 $10,700  

   2                 $11,450                  $11,449

   3                 $12,254                 $12,250

   4                 $13,115                  $13,108

In table we can see Tasha investment will yield more from Thomas.

Thus, Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Tasha’s investment will yield moreover many years because the amount invested at 8% causes the overall total to increase faster.

What is Compound interest?

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest = [tex]\rm P(1+\frac{r}{n} )^{nt}[/tex]

Tasha invests in two different ways

Principal P=$5,000

Rate of Interest r=0.06

Time t=t

n=1

Compound Interest = [tex]\rm P(1+\frac{r}{n} )^{nt}[/tex]

= [tex]\rm 5,000(1+0.06 )^{t}\\\rm 5,000(1.06 )^{t}[/tex]

Principal P=$5,000

Rate of Interest r=0.08

Time t=1

n=1

Compound Interest = [tex]\rm P(1+\frac{r}{n} )^{nt}[/tex]

[tex]\rm 5,000(1+0.08 )^{t}\\\rm 5,000(1.08 )^{t}[/tex]

Total amount yield by Tasha = [tex]5,000(1.06 + 1.08)^{t}[/tex]

Thomas Investment

Principal P=$10,000

Rate r= 0.07

t=t

n=1

Total amount yield by Thomas = 10,000(1.07)^t

here, we will make a table for Tasha and Thomas with different value of t

   t                  Tasha                  Thomas

  1                  $10,700                 $10,700  

  2                 $11,450                  $11,449

  3                 $12,254                 $12,250

  4                 $13,115                  $13,108

Therefore, Tasha’s investment will yield moreover many years because the amount invested at 8% causes the overall total to increase faster.

Learn more about Compound interests here;

https://brainly.com/question/14295570

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