Question

$100 is invested for 20 years. During the first 10 years, the annual rate of 6%. During the last 10 years, the annual rate is 5%. How much interest is compounded during the last 10 years on the interest compounded during the first 10 years (in dollars)?

	A.	Below 5
	B.	Between 5 and 15
	C.	Between 15 and 25
	D.	Between 25 and 35
	E.	Between 35 and 45
	F.	Between 45 and 55
	G.	Between 55 and 65
	H.	Between 65 and 75
	I.	Above 75

Answer 1

The correct answer is F

The Amount is Given by the formulae :Principal * [( 1 + Interest rate ) ^ Number of Years or period]

For First 10 Years = 100 * ( 1+6%)^10

= 100 * (1.06)^10

= 100 * 1.79084

Amount at the end of 10 years = 179.084

Interest Amount = 179.084 - 100

= 79.084

Interest rate compounded of first 10 year at the end of 20 years  = Interest Amount at the end of 10 years * ( 1 + Interest rate) ^ Number of year

= 79.084 * [( 1 + 5%)^10]

= 79.084 * [( 1.05)^10]

= 79.084 * 1.6288

Interest Amount at the end of 20 Years of the first 10 year Interest = 128.812

So, The Compunding of 10 Year interest = 128.812 - 79.084

= 49.728

So, the correct answer is Between 45 and 55.