Question

Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.)

A $50,000 zero-coupon bond maturing in 9 years and selling now for $42,035.

determine the amount due on the compound interest loan. (Round your answers to the nearest cent.)

$14,000 at 4% for 15 years if the interest is compounded in the following ways.

(a) annually
$

caculate the present value of the compound interest loan. (Round your answers to the nearest cent.)

$29,000 after 8 years at 5% if the interest is compounded in the following ways.

(a) annually
  

(b) quarterly

(b) quarterly

Answer 1

Answer to question 1 - Effective rate on bond redeemable at par $50,000 now selling at $ 42,035 due 9 years down the line

Effective interest rate is such a rate at which PV of Inflows = PV of Outflows (refer below image) which is 1.95% also it can be calculated using Interpolation technique which will lead to effective rate of -

Second Question

Question is assumed as PV of Annuity of Compound Interest Loan -

Loan Amount 14,000, Rate - 4%, Compounding - Annually - Period - 15 years

Loan amount = Annuity Amount * PVAF (r=4%, N=15) Using PMT function in excel we arrive at annual payment of $,1259.18 p.a for 15 years The detailed formula is - P = Annutiy, r- rate of interest - n - number of years

Third question

Amount of Loan - 29,000$, r = 5%, n=8 years, compounding - annually (using same formula above)

Under the annual compounding method - $4486.93/p.a for 8 years assuming payment at the end of period.

Under quarterly compounding r= 5%/4=1.25%, n=32 quarters compounding - quarterly, thus using the same formula $ 1105.12/quarter or $ 4,420 per annum.