Question

) Your grandma gave you a $100 10 year savings bond that earns8% interest when you were 8 years old. You are now 15 years old andwould like to cash it in to buy a game.a. How much will you receive if the interest is calculated monthly?b. How much will you receive if the interest is calculated continuously?

Answer 1

The rule of the compounded continuously interest is

`A=Pe^(rt)`

The rule of the compounded monthly interest is

`A=P(1+(r)/(12))^(12t)`

A is the new amount

P is the initial amount

r is the rate in decimal

t is the time in years

Since the initial amount is $100, then

`P=100`

Since the interest rate is 8%, then

`r=(8)/(100)=0.08`

Since the time is from 8 years old to 15 years old, then

`t=15-8=7`

a)

Substitute these values in the second rule above

`\begin{gathered} A=100(1+(0.08)/(12))^(12(7)) \\ A=\text{ \$174.7422051} \end{gathered}`

You will receive about $174.74

b)

Substitute these values in the first rule

`\begin{gathered} A=100e^(0.08(7)) \\ A=\text{ \$}175.06725 \end{gathered}`

You will receive about $175.07