Question

Daniel needs to borrow $25,000 for 5 years. The loan will be repaid in one lump sum at the end of the loan term. Which one is the most beneficial for Daniel?  

		6% compounding interest with annual compouding
		5% compound interest with semiannual compounding
		5% simple interest
		6% simple interest.

Answer 1

a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$25000*(1.06)^5

=$25000*1.338225578

=$33455.64(Approx).

b.We use the formula:
A=P(1+r/200)^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$25000(1+0.05/2)^(2*5)

=$25000*1.280084544

=$32002.11(Approx)

c.Simple interest=Principal*Interest rate*Time period

=(25000*5*5%)=$6250

Hence future value=Simple interest+Principal

=(25000+$6250)=$31250

d.Simple interest=Principal*Interest rate*Time period

=(25000*5*6%)=$7500

Hence future value=Simple interest+Principal

=(25000+$7500)=$32500

Hence the most beneficial is 5% simple interest.