Question

4. A personal loan of $1,000 is made for a period of 18 months at an interest rate of 1.50% per month on the unpaid balance. If the entire amount owed is repaid in a lump sum at the end of that time, determine: a) The effective annual interest rate b) The total amount of interest paid

5. What nominal interest, compounded quarterly, is required to provide a 6% annual effective interest rate? A 12 % annual effective interest rate?

6. How long will it take for $1 to double in value (disregarding any change in the buying power of the dollar) if:

a) The interest rate is 10% compounded annually?

b) The interest rate is 10% compounded semiannually?

c) The interest rate is 10% ordinary simple interest?

Answer 1

Q4
a)
annual effective rate=(1+monthly rate)^12-1=(1+1.5%)^12-1=0.195618171461533

b)
=Loan*monthly rate*number of months
=1000*1.5%*18=270

Q5
nominal rate=((1+annual effective rate)^(1/m)-1)*m

a)
=((1+6%)^(1/4)-1)*4=0.0586953846746372

b)
=((1+12%)^(1/4)-1)*4=0.114949378888321

Q6
Time in years=log(Future Value/Present value)/log(1+r/m)*1/m

a)
=LOG(2)/LOG(1+10%)=7.27254089734171

b)
=LOG(2)/LOG(1+10%/2)*1/2=7.10334954144523

c)
=(2-1)/10%=10