# Loan and Investment Calculations

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Question 1Amount borrowed = \$20,000Rate of interest = 12 % p.a. compounded monthly Monthly payments = Amount borrowed x rate (1+ rate)n / (1+r)n-1Where, rate = monthly rate of interest = 12 % / 12 = 1 % n= no. of monthsNow Monthly payments = 20000 x 1 % (1+ 0.01)8 / (1+0.01)8- 1 =200 x 1.082857 / 1.082857-1 =216.5713 / 0.082857 = \$ 2613.806 Question 2Amount of debt = \$ 120,000To be repaid by quarterly payments for next 3 years Rate of interest = 12 % p.a. compounded quarterly a)Quarterly payment = Amount borrowed x rate / 1- (1+ rate)-nWhere,Rate = quarterly rate of interest = 12/4 = 3 %N= no. of quartersNow quarterly payment = 120000 x 3% / 1- (1+.03)-12 = 3600 / 1- 0.70138 = \$ 12055.45b)Calculation of principal outstanding after 8 quarterly payments= 12055.45[1- (1.03)-4] / 0.03= 12055.45[1-0.888487] / 0.03= 12055.45 x 0.111513 / 0.03= 1344.339 / 0.03= \$ 44811.29

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