Question

Hector's parents anticipate needing $80,000 when he is 18 for his college education. If he is 5 years old now, how much should they invest in an investment plan that pays 6.23% compounded quarterly? Hector ended up getting a full scholarship. His parents agreed to let him draw the interest off the investment account each quarter (3 months) for expenses. How much will Hector receive each quarter?

Answer 1

Answer:

Hectors parent must have invested  $35815.078.

Hector will receive  $1246 each quarter.

Step-by-step explanation:

Given that Amount Required = A = $80000

Time duration = 18 - 5  =13 years

Rate of Interest = 6.23% ( Assuming it is for 1 year )

Also given it is compounded quarterly that is interest is calculated ones in a quarter that is 4 times in  a year

Let say amount to be invested when Hecot is 5 year old = P

Formula for Amount when interest is compounded is given by

A = P ( 1 + R/ 100 )^n

in our case A = $80000

R = Rate of interest  = 6.23 /4 = 1.5575% ( rate of interest for 1 quarter)

n = number of times interest calculated in complete duration

  = 13 * 4 = 52   ( since compounded quarterly , which means  in 1 year , interest is calculated 4 times , so in 13 years , interest is calculated 52 times)

lets put the values in formula

80000 = P( 1 + 1.5575/100)^52

80000 = 2.2336 * P

P = 80000/2.2336= $35815.078

So Hectors parent must have invested  $35815.078.

But good news is hector ended up getting full scholarship and his parents agreed to let him draw the interest off the investment account each quarter.

so Amount is 80000

Rate of interest = 6.23% per year = 6.23/4 = 1.5575% per  quarter

So Quarterly Interest = 1.5575% of 80000 = $1246.

So hector will receive  $1246 each quarter.

 

Answer 2

Hector will receive  $\ 1246$  each quarter.

The formula for compound interest is ;

$A=P\left ( 1+\dfrac{R}{100} \right )^ n$

Compounded quarterly that is we have $4$ quaters in a year

Rate of interest,

$R=\dfrac{6.23\%}{4}\\\\R=1.5575\%$

From $5$ year old till $18$ years we have $13$ years duration.

$n=4*13$ (As $4$ quaters in an year)

$n=52$

Put the value given in the question,

$\ 80000=P\left ( 1+\dfrac{1.5575}{100} \right )^{52}$

$\ 80000=2.2336\times P$

$P=\dfrac{80000}{2.2336}\\\\P=\ 35815.078$

So Hectors parent must have invested $\ 35815.078$

But His parents agreed to let him draw the interest off the investment account each quarter ($3$ months) for expenses

Rate of interest quaterly,

$R=\dfrac{6.23\%}{4}\\\\R=1.5575\%$

Hence the interest calculated quaterly ,

Quaterly interest is:

$1.5575\% \;of\; 80000=\ 1246$

Hector will receive  $\ 1246$  each quarter.

Learn more about Compound interest here:

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