Question

Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account. A ​$2000 deposit in an account with an APR of 3​%. The balance in the account after 1 year is approximately [...]

Answer 1

Future value for continuous compunding = Present value * e^( r*t )

e = 2.7183

r = interest rate = 3%

t = time = 1 year

Future value = 2000 * 2.7183^( 0.03*1 ) = 2061

t = time = 5 years

Future value = 2000 * 2.7183^( 0.03*5 ) = 2323.67

t = time = 20 years

Future value = 2000 * 2.7183^( 0.03*20 ) = 3644.24

Annual percentage yeild for continuos compounding = e^r - 1

e = 2.7183

r = interest rate = 3%

APY = 2.7183^0.03 - 1 = 3.04%

Balance in the account after 1 year = 2061 (as calculated above)