Suppose your firm is seeking a six-year, amortizing $760,000 loan with annual pa

Question

Suppose your firm is seeking a six-year, amortizing $760,000 loan with annual payments and your bank is offering you the choice between a $806,000 loan with a $46,000 compensating balance and a $760,000 loan without a compensating balance. The interest rate on the $760,000 loan is 9.0 percent. How low would the interest rate on the loan with the compensating balance hae to be for you to choose it? interest rate

Suppose your firm is seeking a five year, amortizing $360,000 loan with annual payments and your bank is offering you the choice between a $373,000 loan with a $13,000 compensating balance and a $360,000 loan without a compensating balance. The interest rate on the $360,000 loan is 10.0 percent. How low would the interest rate on the loan with the compensating balance hae to be for you to choose it? interest rate

Explanation / Answer

Question 1

The Annual payment without compensating balance=760000*9%*(1.09^6)/(1.09^6-1)=169419.04

let r be the rate of interest with compensating balance

hence annual payment with compensating balance=806000*r*(1+r)^6/((1+r)^6-1)

now Annual payment with compensating balance <=Annual payment without compensating balance

ie.806000*r*(1+r)^6/((1+r)^6-1)<=169419.04

hence r=7.06%

the interest rate should be as low as 7.06%

Question 2

The Annual payment without compensating balance=360000*10%*(1.10^5)/(1.10^5-1)=94967.09

let r be the rate of interest with compensating balance

hence annual payment with compensating balance=373000*r*(1+r)^5/((1+r)^5-1)

now Annual payment with compensating balance <=Annual payment without compensating balance

ie.373000*r*(1+r)^5/((1+r)^5-1)<=94967.09

hence r=8.63%

the interest rate should be as low as 8.63%

Formula of Annual payment on loan of P at interest rate r for n years

P*r*(1+r)^n/((1+r)^n-1)

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