Question

At the time of her​ grandson's birth, a grandmother deposits $4000 in an account that pays 5% compounded monthly. What will be the value of the account at the​ child's twenty-first​ birthday, assuming that no other deposits or withdrawals are made during this​ period?

Answer 1

Answer:

$874,507,135

Explanation:

To find the final capital, we use the compound interest formula:

Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))

The problem is givining this information:

IC= $4000

i= 5% compounded monthly

n=21 (is it 21 because the grandmother started at the granson´s birth, if she would started when the baby had 1 year, then n=20 and so on)

Before we apply the formula, we have to notice that there is and inconsistency. The interest rate is compounded monthly but n is in years. So, we must change i or n. We will change the interest.

First, we have to transform the periodic interest rate into an Effective Annual rate using this formula:

Effective Annual rate= [(1+periodic interest)^(n)] -1

Effective Annual rate= [(1+5%)^(12)]-1= 79,59%

Now, we can apply the first formula:

FC= $4000*(1+79,59%)^(21)= $874,507,135