Answer:
Option 2 will earn Hannah the most amount of money
$2176.885, 12 years
18 years, $2369.9
N.B: These are the future values of her earnings which is the principal plus compound interests after the respective years. Each compound interest is calculated in the explanation below.
Explanation:
Hannah is trying to select an option to go for in an investment using two different compound interest rate at different years.
To calculate the amount she will accumulate at the end of the respective years using compound interest, we use the formula:
A = P (1 + r/n) ^ nt
Where A= Amount I.e future value of her investment including Interest.
P= Principal amount to be invested
r= annual interest rate
n= number of times the interest was compounded
t= time the money was invested for (in years)
Based on this, let's calculate the earnings for each option Hannah has.
For the first option:
A= ?
P= $1000
r= 6.5% = 0.065
n= 12 (Interest will compound 12 times in 12 years)
t= 12 years
Hence, the formula:
A = 1000 (1 + 0.065/12) ^ 12×12
A= 1000 (1.005416) ^ 144
A= 1000 × 2.1768
A= 2176.8
Hence, the value of Hannah's investment after 12 years at 6.5% interest will be $2176.8.
The compound interest (I) = A - P
= 2176.8 - 1000 = $1176.8
For the second option,
A= ?
P= $1000
r= 4.8% = 0.048
n= 18 (Interest will compound 18 times in 18 years)
t= 18 years
Hence, the formula:
A = 1000 (1 + 0.048/18) ^ 18×18
A= 1000 (1.00266) ^ 324
A= 1000 × 2.3699
A= 2369.9
Hence, the value of Hannah's investment after 18 years at 4.8% interest will be $2369.9
The compound interest (I) = A - P
= 2369.9 - 1000 = $1369.9
Therefore, Hannah should select the first option, because she will earn -$1176.8- money in only -12-years, which is sooner than having to wait for -18- years and a total of -$1369.9- money, which is only a little than the first option.