Answer to Question #171090 in Financial Math for saleemaslam

Question

4.  Amanda borrowed $14,000 at 6.5% compounded semiannually. If the loan is to be repaid in equal semiannual payments over three years and the first payment is due four years after the date of the loan, what is the size of the semiannual payment?  _______________

 

 

 

 

5. How much can be paid in scholarships at the end of each year if $150,000 is deposited in a trust fund and interest is 4.5% compounded annually? _____________

3. Mr. Buffett bought a property by agreeing to make semiannual payments of $12,500 for seven years. If the first payment is due on the date of the purchase and interest is 9% compounded quarterly,

   a. What is the purchase price of the property?  ______________

   b. How much is the cost of financing? ________________

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Answer 1

4.After 4 years Amanda must pay:

$FV=PV(1+r/m)^{mt}$

$FV=14000(1+0.065/2)^{2\cdot4}=\$18082.09$

Let $R$ is the size of the semiannual payment. Then:

$FV=(R(1+i)^n-1)/i,\ n=mt,\ i=r/m$

$R=\frac{iFV+1}{(1+i)^n}=\frac{18082.09\cdot0.065/2+1}{(1+0.065/2)^{3\cdot2}}=\$485.88$

5.It can be paid in 10-years scholarships at the end of each year:

$R=\frac{iFV+1}{(1+i)^n}=\frac{150000\cdot0.045+1}{(1+0.045)^{10}}=\$4347.16$

3.

a) The purchase price of the property:

$FV=12500\cdot7\cdot2=\$175000$

b) The cost of financing: Mr. Buffett must pay quarterly:

$R=\frac{iFV+1}{(1+i)^n}=\frac{175000\cdot0.09/4+1}{(1+0.09/4)^{7\cdot4}}=\$2112.31$