Question

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

Answer 1

Option b- $23,377

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+(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,

`68000=P(1+(0.03575)/(4))^(4* 30)`

`\Rightarrow 68000=P(1.0089375)^(120)`

`\Rightarrow P=(68000)/((1.0089375)^(120))`

`\Rightarrow P=23377.45`

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

Hence, Option b is correct.

Answer 2

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

Solution-

We know that for compound interest,

`A=P(1+(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,

`\Rightarrow 68000=P(1+(0.03575)/(4))^(4* 30)`

`\Rightarrow 68000=P(1.0089375)^(120)`

`\Rightarrow P=(68000)/((1.0089375)^(120))`

`\Rightarrow P=23377.45`

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