Problema Solution
Jake Harris can invest $6,000 for 6 years at National Savings Bank and receive 6% interest compounded annually in a passbook savings account. Moravian Bank offers him 6% interest compounded semiannually. How much more interest will Jake earn if he invests at Moravian?
Answer provided by our tutors
At National Savings Bank:
P = $6000 the principal (the money deposited)
r = 0.06 or 6% annual interest rate
t = 6 years
m = 1 compounding period per year
i = r/m = 0.06/1 = 0.06 interest rate per period
n = t*m = 6*1 = 6 total number of compounding periods
A = the future amount
A = P(1 + i)^n
A = 6000(1 + 0.06)^6
A = $8,511.11
the interest I = A - P = 8,511.11 - 6,000 = $2,511.11
At Moravian Bank:
P = $6000 the principal (the money deposited)
r = 0.06 or 6% annual interest rate
t = 6 years
m = 2 compounding period per year
i = r/m = 0.06/2 = 0.03 interest rate per period
n = t*m = 6*2 = 12 total number of compounding periods
A = the future amountn
A = P(1 + i)^n
A = 6000(1 + 0.03)^12
A = $8,554.57
the interest I = A - P = 8,554.57 - 6,000 = $2,554.57
Jake will earn 2,554.57 - 2,511.11 = $43.46 more interest if he invests in Moravian.