Derek can deposit $211.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 12.00% and compounds interest monthly. Derek can deposit $2,450.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?
Please show how to answer step by step using a financial calculator
For Bank A, it is ordinary annuity with
A = $211
n = 12
t = 10
r = 12% compounded monthly
So, FV = A*((1+r/n)^(n*t) - 1)/(r/n) = 211*((1+0.12/12)^120 - 1)/(0.12/12) = $48538.16
For Bank B, it is also an ordinary annuity with
A = $2450
t = 10 year
FV = same as Bank A = $48538.16
So, FV = A*((1+r)^(t) - 1)/(r) => 48538.16 = 2450*((1+r)^10 - 1)/r
=> r = 14.50%
Bank B must pay a rate of 14.50%
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