Question

1. How many years will it take for $480 to grow to $1,061.07 if​ it's invested at 7 percent compounded​ annually?

The number of years it will take for $480 to grow to $1,061.07 at 7 percent compounded annually is ___ years?

2. At what annual interest​ rate, compounded​ annually, would $520 have to be invested for it to grow to $2,008.76 in 10 years?

The annual interest​ rate, compounded​ annually, at which $520 must be invested for it to grow to $2008.76 in 10 years is ___%

Answer 1

Part 1:

FV = PV (1+r)^n

r - Int Rate per anum

n - Time gap in Years

1061.07 = 480 ( 1+0.07)^n

1.07^n = 1061.07 / 480

= 2.2106

Take Log on both sides

Log(1.07^n ) = Log (2.2106)

Log (a^b) = b * log (a)

n * Log (1.07 ) = log (2.2106)

n * 0.0294 = 0.3445

n = 0.3445 / 0.0294

= 11.72 Years

Part 2:

FV = PV (1+r)^n

r - Int Rate per anum

n - Time gap in Years

2008.76 = 520 (1+r)^10

(1+r)^10 = 2008.76 / 520

= 3.863

1+r = 3.863^(1/10)

= 1.1447

r = 1.1447 - 1

= 0.1447 i.e 14.47%

Plz comment, if any further assistance is required