Question

Business Applications. Find the present value (principal) or the compound interest, as indicated. Use a calculator or Table 16-1 or Table 16-2 to find FVF or PVF. Round answers to the nearest cent. show entire solution please.

16. Bill Starnes needs to buy another used logging truck. His mother will loan him part of the money at 3% compounded quarterly. If Bill estimates that he will be able to repay his mother a total of $30,000 in 2 1/2 years, how much can he borrow from her today?

18. John Burnett wants to have $30,000 available at the end of 3 years to help purchase a computerized metal lathe for his machine shop. If John can invest money at 6% compounded semiannually, how much should he invest?

20. Erin Bernstein estimated that she would need $18,000 in 2 years to buy new equipment for her pottery shop. Having extra cash, she invested money in an investment that advertised a return of 6% com-pounded semiannually. Erin invested just enough money to end up with the $18,000. How much of the $18,000 did Erin earn on her investment?

Answer 1

Solution:

Given,

1st case

16.Bill Starnes needs to buy another used logging truck. His mother will loan him part of the money at 3% compounded quarterly. If Bill estimates that he will be able to repay his mother a total of $30,000 in 2 1/2 years, how much can he borrow from her today is to calculated,

We know that,

PV= FV/(1+r/m)n*m

Where,

PV= present value,

FV= future value,

m= compounded,

r= annual interest rate,

n= number of years

Hence,

PV= $30,000/(1+0.03/4)2.5*4

= $27840.09

Therefore, he borrow $27840.09 from her today.

2nd case

Given,

18.John Burnett wants to have $30,000 available at the end of 3 years to help purchase a computerized metal lathe for his machine shop. If John can invest money at 6% compounded semiannually, how much should he invest is to be calculated,

Similarly as above calculation,

PV = $30,000/(1+0.06/2)3*2

= $25,124.53

Therefore he should invest $25124.53.

3rd case

Given,

20. Erin Bernstein estimated that she would need $18,000 in 2 years to buy new equipment for her pottery shop. Having extra cash, she invested money in an investment that advertised a return of 6% com-pounded semiannually. Erin invested just enough money to end up with the $18,000. How much of the $18,000 did Erin earn on her investment is to be founded,

Similarly as above calculation,

PV= $18000/(1+0.06/2)2*2

= $15992.77

Therefore, of the $18000 Erin earned $2007.23 on her investment.

Note: Answer are rounded off to 2 decimals for calculation purpose.