Question

1. Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding.Determine the amount that the investment is worth at the end of the given time period.

P = $6000, t = 14 years

a.) 3% interest

b.) 4% interest

c.) 4.5% interest

Bethany needs to borrow $11,000. She can borrow the money at 4.5% simple interest for 4 years OR she can borrow at 5% with interest compounded continuously for 4 years.

a.) How much total interest would Bethany pay at 4.5% simple interest?

b.)How much total interest would Bethany pay at 5% interest compounded continuously?

c.)Which option results in less total interest ?

Answer 1

1.

In this question, Amount has to be calculated using Compound Interest Formula as interest is compounded continuously.

So, Formula of calculating Amount in case of Compound Interest is as follows:

Amount=P(1+R/100)^t

Here, P=Principal

R= Rate of interest at which the interest is compounded

t= Time for which the principal amount has been invested

And, as per question:

P=$6000

t=14

THEREFORE, according to formula:

a)At 3%

Amount= 6000(1+3/100)¹⁴

= 6000(1.03)¹⁴

= 6000(1.512)

= $9072

b) at 4%

Amount =6000(1+4/100)¹⁴

=6000(1.04)¹⁴

=6000(1.732)

=$10392

c) at 4.5%

Amount= 6000(1+4.5/100)¹⁴

=6000(1.045)¹⁴

=6000(1.852)

=$11112