Question

Suppose you deposit $12,000 in an account that offers 1.7% annual interest, as long as you
leave the principal untouched for 5 years.
(a) If interest is compounded quarterly, what would the account be worth after 5 years?

FORMULA:

SOLUTION:

(b) If interest is compounded continuously, what would the account be worth after 5 years?

FORMULA:

SOLUTION:

(c) Is the effective interest rate for either scenario greater or less than 1.7%? Explain your
answer.

5. (a) (4 points) Nick has the opportunity to invest in a venture that is guaranteed to pay 3%
annually, compounded monthly. His money will be tied up for 5 years. How much does Nick
have to invest today in order for it to grow to $9000?

FORMULA:

SOLUTION:

(b) (6 points) Marielle invests $1250 at 3% in an account that compounds interest
continuously. How long would it take for it to grow to $2000?

FORMULA:

SOLUTION:

Answer 1

Suppose you deposit $12,000 in an account that offers 1.7% annual interest, as long as you
leave the principal untouched for 5 years.
(a) If interest is compounded quarterly, what would the account be worth after 5 years?

Answer)

(b) If interest is compounded continuously, what would the account be worth after 5 years?

(c) Is the effective interest rate for either scenario greater or less than 1.7%?

Yes, effective interest rate is greater than 1.7% in both cases when interest is compounded quarterly and continuously

Continuous compounding means compound every instant, consider investment of 1$ for 1 year at 100% interest rate.

Question 5)

Part (A)

Part (B)

it will take 15.66 yrs for $ 1250 to grow into $ 2000 when interest rate is 3% compounded continuously