Please explain step by step Find the amount A in a savings a

Please explain step by step

Find the amount, A, in a savings account it $2000 is invested at 7% for 4 years and disinterest is compounded: annually semiannually quarterly daily (use 360 days) continuously

Solution

Solution:

Formula

Savings amount F= $ 2000

Interest rate r = 7%

time t = 4 years

Compounded amount = A = ?

Calculation of A if Compounded annually

time periods = 4 annual years

A = F (1+r)^t

= 2000 (1+0.07)⁴

= 2000(1.31)

= $ 2620

Calculation of A if compounded Semi annually

Time periods = t = 4*2 = 8

Interest Rate = 7%/2

= 3.5%

= 2000(1+0.035)⁸

= 2000(1.316)

= $ 2632

Calculation of A if Compounded Quarterly

Time Period t = 4*4 = 16

Interest Rate = r = 7%/4 = 0.0175

= 2000(1+0.0175)¹⁶

= 2000(1.32)

= $ 2640

Calculation of A if compounded Daily

Time Period t = 7%/365 = 0.00019

Interest Rate r = 4*360 = 1440

= 2000(1+0.00019)¹⁴⁴⁰

= 2000(1.315)

= $ 2630

Calculation of A if compounded Continuously

Time Period t = 7%/

Interest Rate r = 4*

A = P e^rt

= 2000 * e^4*7%

= 2000*1.323

= $ 2646