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# Calculating the loan amount

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Suppose you are a loan officer for a bank. A start-up company has qualified for a loan. You are pondering various proposals for repayment:

1. Lump sum of \$500,000 four years hence. How much will you lend if your desired rate of return is:

a. 12%, compounded annually?
b. 16%, compounded annually?

2. Repeat number 1, but assume that the interest rates are compounded semiannually.

3. Suppose the loan is to be paid in full by equal payments of \$125,000 at the end of each of the next 4 years. How much will you lend if your desired rate of return is:

a. 12%, compounded annually?
b. 16%, compounded annually?

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#### Solution Preview

Suppose you are a loan officer for a bank. A start-up company has qualified for a loan. You are pondering various proposals for repayment:

1. Lump sum of \$500,000 four years hence. How much will you lend if your desired rate of return is:
a. 12%, compounded annually?

Amount to be returned after 4 years=FV=\$500,000
Number of periods=n=4 (years)
Rate of return=r=12% (annual)
Amount that can be given =Present value of \$500,000 to be received after 4 years=PV=?

PV=FV/(1+r)^n=500000/(1+12%)^4=\$317,759

b. 16%, compounded annually? ...

#### Solution Summary

Solution describes the steps to calculate loan amount at two different rate of interest in case a lump sum amount is to be received after loan period. It also calculates loan amount at two different rate of interest in case repayment is done by equal annual payments.

\$2.19