Question

How much money would need to be deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000? a. $75,425.52 b. $59,130.43 c. $21,009.20 d. $20,258.70

Answer 1

I will assume you are using compound interest.

let the amount invested be x

x(1.0575)^25 = 85000
x = 85000/1.0575^25 = $21,009.20

Answer 2

c. $21009.20

Explanation:

We are asked to find the principal amount of money that would be needed to deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nT)`, where,

A = Final amount after T years,

P = Principal amount,

r = Interest rate in decimal form,

n = Number of times interest is compounded per year,

T = Time in years.

Let us convert our given interest rate in decimal form.

`5.75\%=(5.75)/(100)=0.0575`

Upon substituting our given values in compound interest formula we will get,

`\$85,000=P(1+(0.0575)/(1))^(1*25)`

`\$85,000=P(1+0.0575)^(25)`

`\$85,000=P(1.0575)^(25)`

`\$85,000=P*4.0458464965061301`

Let us divide both sides of our equation by 4.0458464965061301.

`(\$85,000)/(4.0458464965061301)=(P*4.0458464965061301)/(4.0458464965061301)`

`\$21009.20044134235=P`

Upon rounding our answer to nearest hundredth we will get,

`P\approx \$21009.20`

Therefore, an amount of $21009.20 should be deposited in the account and option 'c' is the correct choice.