Question

Manish, a bank employee, purchased a plot (15m × 18m) in Ghaziabad. He paid ₹ 2,00,000 at the beginning as down payment and agreed to pay the remaining ₹ 6,00,000 at the end of 2 years from the date of purchase.

In order to pay ₹ 6,00,000 at the end of two years, he opened an R.D. account in his bank, with ₹ 20,000 per month at 8% rate of interest.

1. Find the maturity value of this account at end of 2 years.
2. Is the M.V. of the above R.D. account equal to ₹ 6,00,000?

If not, how much more/less should the monthly instalment be so that Manish gets the required money (₹ 6,00,000) at the end of two years?

Answer 1

(i) Given,

n = 2 years = 24 months,

P = ₹ 20,000,

r = 8%

∴ I = `P xx (n(n + 1))/(2 xx 12) xx r/100`

Substituting values we get:

∴ I = `20,000 xx (24(25))/24 xx 8/100`

= `20,000 xx 25 xx 8/100`

= 20,000 × 2

= ₹ 40,000

Maturity Value (M.V.) = Sum deposited + Interest

= ₹ 20,000 × 24 + ₹ 40,000

= ₹ 5,20,000.

Hence, the maturity value of this account at end of 2 years = ₹ 5,20,000.

(ii) Maturity value of the R.D. account is ₹ 5,20,000.

So the maturity value is not equal to ₹ 6,00,000.

= ₹ 6,00,000 − ₹ 5,20,000 

= ₹ 80,000

So, Manish gets ₹ 80,000 less.

Thus, the M.V. of the above R.D. account is not equal to ₹ 6,00,000.

Let required monthly instalment be x.

I = `P xx (n(n + 1))/(2 xx 12) xx r/100`

Substituting values we get:

∴ I = `x xx (24(25))/24 xx 8/100`

= 2x

Maturity value = 24x + 2x = 26x

Since required M.V. = 6,00,000

26x = 6,00,000

`x = (6,00,000)/26`

x  = 23,076.92 ≈ ₹ 23,077.

Difference in monthly instalment = ₹ 23,077 − ₹ 20,000

= ₹ 3,077.

Hence, monthly instalment should be ₹ 3,077 more per month to get ₹ 6,00,000 at the end of two years.