Mathematics, 16.04.2020 06:21 jhashknkughb6759

Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Your answer is t=

Answers: 1

Show answers

Answers

The time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year is 2.06 months

The formula for calculating the compound interest is expressed as:

$A = P(1+\frac{r}{n} )^{nt$

A is the future value = $6000

P is the amount invested = $5000

r is the rate (in %) = 7.5% = 0.075

t is the time taken (in years)

n is the time of compounding = 4

Substitute the given parameters into the formula:

$6000 = 5000(1+\frac{0.075}{4} )^{4t}\\\frac{6}{5} =(1+0.3)^{4t}\\1.2=(1.3)^{4t}\\log 1.2 = 4tlog1.4\\4t =\frac{log1.2}{log1.4}\\4t= \frac{0.07918}{0.1139}\\4t = 0.6951\\t = \frac{0.6951}{4}\\t= 2.08 months$

This shows that the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year is 2.06 months

Learn more here:link

Answer from: lorilhuff8197

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Step-by-step explanation:

The given is,

Initial investment - $5000

Future amount - $6000

Interest rate - 7.5% (compounded quarterly)

Step:1

Formula to calculate the Future amount with compound interest,

$F = P(1+\frac{r}{n} )^{nt}$ ...................................(1)

Where, F - Future amount

P - Initial amount

r - Rate of interest

n - No. of compounding in a year

t - Time period

From given,

F = $6000

P = $5000

r = 7.5%

n = 4 (compounded quarterly)

Equation (1) becomes,

$6000=5000(1+\frac{0.075}{4} )^{(t)(4)}$

$\frac{6000}{5000} =(1+0.01875)^{4t}$

$1.2 = (1.01875)^{4t}$

Take log on both sides,

log 1.2 = 4(t) log 1.01875

Substitute log values,

0.07918 = 4(t) (0.0080676)

= (t) (0.0322705)

$t = \frac{0.07918}{0.0322705}$

= 2.45

t ≅ 2.5 years

Result:

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Answer from: Quest

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

Answer from: Quest

true

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 20:30

Wrote and expression for the difference of p and 4

Answers: 1

Answer

Mathematics, 21.06.2019 20:40

If the endpoints of the diameter of a circle are (8, 6) and (2,0), what is the standard form equation of the circle? a) (x + 5)2 + (y + 3)2 = 18 (x + 5)2 + (y + 3)2 = 3.72 (x - 5)2 + (y - 3)2 = 18 d) (x - 5)2 + (y - 3)2 = 32

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

On this question. a hypothermia occurs when a person's body temperature drops below 95 degrees fahrenheit. write and solve an inequality that describes how much lower the body temperature of a person with hypothermia will be than the body temperature of a person with a normal temperature of 98.6 degrees fahrenheit

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Suppose the equation ||x-a|-b|=2008 has 3 distinct real roots and a not =0. find the value of b.

Answers: 1

Answer

You know the right answer?

Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate...

Questions

Mathematics, 27.07.2019 03:30

Scott is 7 years older than stephanie. in 3 years the sum of their ages will be 59. how old is scott now?...

Mathematics, 27.07.2019 03:30