Question

Determine how much is in each account on the basis of the indicated compounding after the specified years have passed; P is the initial principal, and r is the annual rate given as a percent. (Round your answers to the nearest cent.) after one year where P = $7100 and r = 8.8%

(a) compounded annually $________

(b) compounded quarterly $_______

(c) compounded monthly $_______

(d) compounded weekly $_______

(e) compounded daily $________

Answer 1

Future Value (FV) = P x (1+i)ⁿ

where n is number of periods.

and i is rate per period n

Initial Principal (P) = $7,100

Annual rate of interest (r) = 8.8%

To Find: Value after 1 year

(a) If annual rate is compounded annually,

P = $7,100

i = 8.8%

n = 1

Therefore, FV = 7100 x (1+0.088)¹

Therefore, FV = $7,724.80

(b) If annual rate is compounded quarterly,

P = $7,100

i = 8.8% / 4 = 2.2%

n = 1 x 4 = 4

Therefore, FV = 7100 x (1+0.022)⁴

Therefore, FV = $7,745.72

(c) If annual rate is compounded monthly,

P = $7,100

i = 8.8% / 12 = 0.7333%

n = 1 x 12 = 12

Therefore, FV = 7100 x (1+0.0073333)¹²

Therefore, FV = $7,750.63

(d) If annual rate is compounded weekly,

P = $7,100

i = 8.8% / 52 = 0.1692%

n = 1 x 52 = 52

Therefore, FV = 7100 x (1+0.001692)⁵²

Therefore, FV = $7,752.54

(e) If annual rate is compounded daily,

P = $7,100

i = 8.8% / 365 = 0.0241%

n = 1 x 365 = 365

Therefore, FV = 7100 x (1+0.000241)³⁶⁵

Therefore, FV = $7,753.03