# GMAT Math Questions | Interest Q20

#### Compound Interest | Equated Annual Installments | Word Problem

The given question is a GMAT problem solving question from the topic Interest. It tests the concept of finding present value of future payments. A medium difficulty, GMAT 650 level sample question in interests.

Each of the Annual payments will be $x Rate of interest, r = 7% p.a = $$frac{7}{100}$ = 0.07 Investment Period: John will receive the first payment of$x after two years. Let the present value of first payment be $y. John will receive the second payment of same$x one year after the first payment. Let the present value of the second payment by z. #### Step 2 : Compute the Present value of individual payment Formula for the future value: FV = PV$1 + r)n
PV is the present value; FV is the future value; r is the rate of interest and n is the number of years.

Present value of the First payment:
FV = x; PV of the first payment = y; r = 0.07; n = 2
Therefore, y(1 + 0.07)2 = x
Or y = $$frac{x}{$1 + 0.07$^2})
y = $$frac{x}{$1.07$^2})

Present value of the Second payment:
FV = x; PV of second payment = z; r = 0.07; n = 3
Therefore, z(1+ 0.07)3 = x
Or z = $$frac{x}{$1 + 0.07$^3})
z = $$frac{x}{$1.07$^3})

#### Step 3 : Compute the combined Present value of payments

Present value of the two payments:
PV = y + z
PV = $$frac{x}{$1.07$^2}) + $$frac{x}{$1.07$^3})
PV = $$frac{1.07x}{$1.07$^3}) + $$frac{x}{$1.07$^3})
Present value of two payments = $$frac{2.07x}{$1.07$^3})

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## Additional Practice Questions in Ratio Proportion, Mixtures, Percents, Fractions, Profits, and Interest

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