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=

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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

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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

mxb67

step-by-step explanation:

Answer from: Quest

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s

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