Given that Amber borrows $1,450 from the bank.
She has two options to pay the loan amount. Pay in 3 years or in 2 years.
Calculation of interest for payment in 3 years.
Loan amount P=1450
Interest rate r=5%=0.05
Time t=3 years
Interest is compounded annually so we will use compound interest formula
[tex] A=P(1+r)^t [/tex]
Plug the given value
[tex] A=1450*(1+0.05)^3 [/tex]
[tex] A=1450*(1.05)^3 [/tex]
[tex] A=1450*1.157625 [/tex]
A=1678.55625
Interest = A-P=1678.55625-1450= 228.55625
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Calculation of interest for payment in 2 years.
Loan amount P=1450
Interest rate r=3.5%=0.035
Time t=2 years
Interest is compounded annually so we will use compound interest formula
[tex] A=P(1+r)^t [/tex]
Plug the given value
[tex] A=1450*(1+0.035)^2 [/tex]
[tex] A=1450*(1.035)^2 [/tex]
[tex] A=1450*1.071225 [/tex]
A=1553.27625
Interest = A-P=1553.27625-1450= 103.27625
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Now we just have to find the difference of interest in both cases
228.55625-103.27625 = 125.28
Hence final answer is approx $125.
