show all of your work to arrive a final result Simple Interest Simple Interest, I = P *n * 1 I- Simple Interest P Principal (amount borrowed or lent) Final Amount, F P-P Pni n-number of interest periods i- simple interest rate Compound Interest Factors 1interest rate n = number of interest (compounding) periods P- present sum (initial principal amount) (F/P): Algebraic Notation: FP(1 i)\" A- an equal periodic amount (uniform series) F-a future sum (P/F): Algebraic Notation: P F(1 i) (A/F): Algebraic Notation: A F (AP): Algebraic Notation : A- (A/G): Algebraic Notation: G (P/G): Algebraic Notation: G2 Factor Notation: F - P(F/P i, n Factor Notation: P -F(P/F i,n A A(F/A i, n (F/A): Algebraic Notation: F Factor Notation: F Factor Notation: A-F(A/F i,n (P/A): Algebraic Notation: P A (P/A): Algebraic Notation: PAR Factor Notation: PA(P/A i,n Factor Notation: A -P(A/P i,n (NG): Factor Notation : A A1 ± G(A/G í, n) A1 Constant amount G-Gradient amount (P/G): Factor Notation: A1(P/A i,n)t G(P/G i, n) Interest Rate Conversion: 7 Effective Interest Rate, i - Effective Annual Interest rate, ( 1 + Nominal Interest Rate, rc(1 + i)c) - 1 Continuous Interest Factors: Pe\" PF/P i, n] (F/P): Algebraic Notation: F (P/F): Algebraic Notation: P- F (A/F): Algebraic Notation: A F (A/P): Algebraic Notation: A P Factor Notation: F Factor Notation: PFP/F i,n (F/A): Algebraic Notation: FAT (em-1) Factor Notation: F -A|F/A i,n Factor Notation: A- F[A/Fi,n (1 71 (P/A): Algebraic Notation: P-A Factor Notation: P A[P/A i, n Factor Notation: A = P [A/P i, n Solution In both the cases, the amount deposited in the bank (P) = $5000 and the time is 6 years. a) When the interest is compounded quarterly, the formula of the Amount (A) is: A = P{1+ (r/n)}nt where r is the interest rate, n is the number of times interest is compounded per year and t is the time in years. Here t=6 years, n= 4 and r = 12% p.a or 12/100 = 0.12. Therefore, A = 5000 (1+(0.12/4)4*6 A = $10,163.97 Thus the interest received when interest is compounded quarterly is $10163.97-$5000 = $5163.97 b) When the interest is compounded continuously, the formula of the Amount (A) is: A = P*ert where r is the interest rate and t is the time in years. For this example r = 10% or 10/100 = 0.10. Therefore, A = 5000*e(0.10*6) Or A = $9110.59 Therefore the interest received when interest is compounded continuously is $9110.59 - $5000 = $4110.59.

1. show all of your work to arrive a final result Simple Interest Simple Interest, I = P *n * 1 I-
Simple Interest P Principal (amount borrowed or lent) Final Amount, F P-P Pni n-number of
interest periods i- simple interest rate Compound Interest Factors 1interest rate n = number of
interest (compounding) periods P- present sum (initial principal amount) (F/P): Algebraic
Notation: FP(1 i)" A- an equal periodic amount (uniform series) F-a future sum (P/F): Algebraic
Notation: P F(1 i) (A/F): Algebraic Notation: A F (AP): Algebraic Notation : A- (A/G):
Algebraic Notation: G (P/G): Algebraic Notation: G2 Factor Notation: F - P(F/P i, n Factor
Notation: P -F(P/F i,n A A(F/A i, n (F/A): Algebraic Notation: F Factor Notation: F Factor
Notation: A-F(A/F i,n (P/A): Algebraic Notation: P A (P/A): Algebraic Notation: PAR Factor
Notation: PA(P/A i,n Factor Notation: A -P(A/P i,n (NG): Factor Notation : A A1 ± G(A/G í, n)
A1 Constant amount G-Gradient amount (P/G): Factor Notation: A1(P/A i,n)t G(P/G i, n)
Interest Rate Conversion: 7 Effective Interest Rate, i - Effective Annual Interest rate, ( 1 +
Nominal Interest Rate, rc(1 + i)c) - 1 Continuous Interest Factors: Pe" PF/P i, n] (F/P):
Algebraic Notation: F (P/F): Algebraic Notation: P- F (A/F): Algebraic Notation: A F (A/P):
Algebraic Notation: A P Factor Notation: F Factor Notation: PFP/F i,n (F/A): Algebraic
Notation: FAT (em-1) Factor Notation: F -A|F/A i,n Factor Notation: A- F[A/Fi,n (1 71 (P/A):
Algebraic Notation: P-A Factor Notation: P A[P/A i, n Factor Notation: A = P [A/P i, n
Solution
In both the cases, the amount deposited in the bank (P) = $5000 and the time is 6 years.
a) When the interest is compounded quarterly, the formula of the Amount (A) is:
A = P{1+ (r/n)}nt where r is the interest rate, n is the number of times interest is compounded
per year and t is the time in years.
Here t=6 years, n= 4 and r = 12% p.a or 12/100 = 0.12.
Therefore, A = 5000 (1+(0.12/4)4*6
A = $10,163.97
Thus the interest received when interest is compounded quarterly is $10163.97-$5000 =
$5163.97
b) When the interest is compounded continuously, the formula of the Amount (A) is:
A = P*ert where r is the interest rate and t is the time in years.
For this example r = 10% or 10/100 = 0.10.
Therefore, A = 5000*e(0.10*6)
Or A = $9110.59
Therefore the interest received when interest is compounded continuously is $9110.59 - $5000 =

2. $4110.59