Question

On a child’s first day of kindergarten, a deposit of $7,500 is made in a trust fund that pays 3.75% interest, compounded continuously. What is the balance in this account on the child’s 13th birthday?

Answer 1

The balance of the account on the child's 13th birthday would be $101,225.67

Continuous compounding mean that the interest in the account is compounded infinitely over a period of time

The formula for calculating future value of an amount when the interest is compounded continuously is: $PV. e^{r} N$

Where

• PV = amount deposited = $7500

• e = 2.7182818
• N = number of years = 13
• r = interest rate = 3.75%

$7500 x $2.7182818^{0.0375}$ x 13 = $101,225.67

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