Answered

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it has an accumulated value of $68,000 at the end of 30 years?

a.

$23,706

b.

$23,377

c.

$52,069

d.

$58,944

Verified Answer :

InesWalston

Answer-

$23377 must be deposited to get $68000 at the end of 30 years.

Solution-

We know that for compound interest,

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

Where,

A = Future amount = $68,000

P = ??

r = 3.575% annual = 0.03575

n = 4 as interest is compounded quarterly

t = time in year = 30 years

Putting the values,

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Therefore, $23377 must be deposited to get $68000 at the end of 30 years.

Answer:

Option b- $23,377

Step-by-step explanation:

Given : An account earning 3.575% interest compounded quarterly so that it has an accumulated value of $68,000 at the end of 30 years.

To find : How much principal would need to be placed into an account?

Solution :

Using compound interest formula,

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

Where,

A = Future amount = $68,000

P = Principal value =?

r = 3.575% annual = 0.03575

n = 4  (interest is compounded quarterly)

t = time in year = 30 years

Putting the values,

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Therefore, $23,377 must be deposited to get $68000 at the end of 30 years.

Hence, Option b is correct.

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