a Construct an equation to model the amount of money in your

a. Construct an equation to model the amount of money in your account.

b. How much did your aunt put in initially?

Solution

let R be the rate of interest

P be the principle amount and n be the time

Interest = (PnR)/100

A(n) is the amount of money int he account after n years

==> A(n) = P + (PnR)/100

After 2 years amount in the account is $8070

==> P + (P(2)R)/100 = 8070

==> 100P + 2PR = 807000 -------- (1)

After 5 years amount in the account is $9225

==> P + (P(5)R)/100 = 9225

==> 100P + 5PR = 922500 --------- (2)

solving (1) and (2)

(2) - (1) ==> 100P + 5PR - (100P + 2PR) = 922500 - 807000

==> 3PR = 115500

==> PR = 38500

==> R = 38500/P ----------- (3)

Substitute R = 38500/P in (1)

==> 100P + 2P(38500/P) = 807000

==> 100P + 77000 = 807000

==> 100P = 730000

==> P = 730000/100

==> P = 7300

Hence She put $ 7300 initially

substitute P in (3)

==> R = 38500/7300

==> R = 5.27397

==> A(n) = 7300 + (7300*5.27397*n)/100

c) n = 10 years

==> A(10) = 7300 + (7300*5.27397*10)/100

==> A(10) = $11149.998

Hence money in the account after 10 years = $11149.998