Lori borrowed 3000 from a local bank for 240 days at a simpl

Lori borrowed $3000 from a local bank for 240 days at a simple interest rate of 8.1% a) What was the total that she paid on the day it was due? b) How much interest did she pay for the use of the money? 3. a) When saving to take a vacation around the world Keon invests $250 monthly in an annuity with 9% interest compounded monthly. Determine the amount in ordinary the account after 10 years. How much would be in the account after 10 years if interest was compounded continuously? b)

Solution

Question 2

a) We have

A = P (1+rt)

where

A - Matured amount

P - Principal

r - rate

t - time

A = 3000 * (1+(.081*240/365))

= 3000 * 1.0533

= $3159.78

b) Interest Paid = Matured amount - principal

= 3159.78 - 3000

= $159.78

Question 3

a) Future value of Annuity = A [((1+r)ⁿ-1) / r]

Where

A - regular payment (here 250)

r - rate per period (here 9%/12 = .75%, since compounded monthly)

n - no. of periods (here 10*12=120, since compounded monthly)

Future value of Annuity =250 [(1.0075¹²⁰-1) / .0075]

= 250 * [( 2.4514 - 1)/.0075

= 250 * 193.52

= $48,380

b) Interest is compounded continuosly means each period interest is added to principal and interest is not only on principal but on interest portion also.

Future value of Annuity (continuos compounding) = Cashflow * [(e^rt-1)/(e^r-1)]

Where

r - rate per period (here 9%/12 = .75%, since compounded monthly)

n - no. of periods (here 10*12=120, since compounded monthly)

Future value of Annuity (continuos compounding) = 250 * [(e^.9-1)/(e^.0075-1)]

= 250 * [(2.45960-1)/(1.0075-1)]

= 250 * 194.6133

= $48,653.33