Question

How many years will it take to make your investment $10,000 to $15,000 when interest rate = (Y+3) %?(if Y=4)

Answer 1

Here, 

Future Value, FV = 15000$

Present Value, PV = 10000$

rate of interest, i = (Y+3)% = (4+3)% = 7% = 0.07

number of years, n = ?

the formula: FV = PV(1+i)ⁿ

∴ 15000 = 10000(1+0.07)ⁿ

=> (1.07)ⁿ = 15000/10000 = 1.5

=> ln(1.07)ⁿ = ln(1.5) [∵take ln in both sides]

=> nln(1.07) = ln(1.5)

=> n = ln(1.5)/ln(1.07) = 5.99 ～6 years

Answer 2

SOLUTION :

Interest rate, r = Y + 3 %  and Y = 4 %

=> Interest rate, r = 7 % = 0.07

=> 1 +  r = 1.07

If it is simple interest rate , then,

FV = PV( 1 + r t) 

=> 15000 = 10000 ( 1 + 0.07 t)

=> t = (15000/10000 - 1)/0.07

=> t = 7.14 years approx.

At simple interest rate of 7%, it will take 7.14 years to grow $10000 to $15000 . (ANSWER)

If compounded annually, then,

FV = PV( 1 + r)^t

=> 15000 = 10000 (1 + 0.07)^t

=> (1 + r)^t = 15000 / 10000 = 1.5

Taking log on both sides :

=> t log (1+ r) = log(1.5)

=> t log(1.07) = log(1.5)

=> t = log(1.5) / log(1.07)

=> t = 5.99 years 

At annual compounding, $10000 will grow to $15000 @ 7% = 5.99 years (ANSWER)