6. Joe & Sally want to purchase $6,750 worth of furniture from Olum’s, using in

Question

6. Joe & Sally want to purchase $6,750 worth of furniture from Olum’s, using in store financing. The financing program requires 3 years of monthly payments in the form of an annuity due. The APR on this financing is 8.4%, compounded monthly. What will their monthly payment be?

7. Twenty years ago Seth purchased an investment for $14,990. Today that same investment is valued at $55,000. If the average annual rate of inflation over the past twenty years has been 3.1%, what is the real return on this investment?

Explanation / Answer

6.

Formula for PV of annuity due can be used to compute monthly installment as:

PV = P + P x [1-(1+r)-(n-1)/r]

PV = Present value of annuity = $ 6,750

P = Periodic payment

r = rate per period = 8.4 % p.a. or 0.084/12 = 0.007 p.m.

n = No. of periods = 3 years x 12 months = 36 periods

$ 6,750 = P + P x [1 – (1+0.007)-(36-1)/0.007]

$ 6,750 = P + P x [1 – (1.007)-35/0.007]

$ 6,750 = P + P x [(1 – 0.783372876792174)/0.007]

$ 6,750 = P + P x (0.216627123207826/0.007)

$ 6,750 = P + P x 30.94673189

$ 6,750 = P x (1 + 30.94673189)

$ 6,750 = P x 31.94673189

P = $ 6,750/31.94673189

P = $ 211.2892181 or $ 211.29

Monthly payment will be $ 211.29

7.

Nominal rate of return can be computed using formula for compound interest as:

A = P x (1+r) n

A = Future value of investment (i.e value today) = $ 55,000

P = Principal amount = $ 14,990

r = Rate per period (nominal rate)

n = No. of periods = 20

$ 55,000 = $ 14,990 x (1+r) 20

$ 55,000/$ 14,990 x (1+r) 20

$ 55,000/$ 14,990 = (1+r) 20

1 + r = ($ 55,000/$ 14,990)1/20

1 + r = (3.669112742)0.05

1 + r = 1.06715635

r = 1.06715635 – 1 = 0.06715635 or 6.72 %

(1+real returns) x (1+inflation) = 1 + nominal returns

(1+ real returns) x (1+0.031) = 1 + 0.06715635

(1+ real returns) x (1.031) = 1.06715635

(1+ real returns) = 1.06715635/1.031

(1+ real returns) = 1.035069204

Real returns = 1.035069204 -1

Real returns = 0.035069204 or 3.51 %

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.