FNAN 301
Solutions to lab problems – 1/28/2011
Group lab problem (Summer C 2010, quiz 1, question 2, version 2)
Clint just deposited $19,500 in an account that will earn 8.1 percent per year in compound
interest for 12 years.
If Mona deposits $19,500 in an account in 1 year from today that earns
simple interest, then how much simple interest per year must Mona earn to have the same
amount of money in 12 years from today as Clint will have in 12 years from today?
Timeline
Time
Today
in 1 yr
in 2
yrs
in 3
yrs
in 4
yrs
in 5
yrs
in 6
yrs
in 7
yrs
in 8
yrs
in 9
yrs
in 10
yrs
in 11
yrs
in 12
yrs
Time
0
1
2
3
4
5
6
7
8
9
10
11
12
Clint
invest
19,500
Mona
invest
19,500
Mona
re-time
0
1
2
3
4
5
6
7
8
9
10
11
Solve in 2 steps:
1. Compute how much Clint will have in 12 years
2. Compute the simple interest rate needed by Mona to have the same amount in 12 years
1. Compute how much Clint will have in 12 years
With Clint, C
0
= 19,500; r = .081, and t = 12
In 12 years, Clint will have C
0
× (1+r)
t
= 19,500 × (1.081)
12
= $49,652.71
2. Compute the simple interest rate needed by Mona to have the same amount in 12 years
If Mona deposits $19,500 in 1 year from today, and she wants to have $49,652.71 in 12 years, then
she needs to earn total interest of $49,652.71 – $19,500 = $30,152.71 over the 11 years between 1
year from today and 12 years from today
To earn $30,152.71 over 11 years, she needs to earn [$30,152.71 / 11] = $2,741.16 in interest per
year, since the same amount of interest is earned each year with simple interest
The simple interest rate would be equal to the interest earned per year divided by the initial
amount of the investment = [$2,741.16 / $19,500] = 14.057% per year
Alternatively, if you earn simple interest, then C
0
today will grow to be worth the following in t
periods: C
0
× (1 + (simple interest rate per period × t))
Therefore, since Mona expects to deposit $19,500 in 1 year from today and she wants to have
$49,652.71 in 12 years from today, which is 11 years later, the required simple rate can be found as
$49,652.71 = $19,500 × (1 + (simple interest rate per period × 11))
49,652.71 / 19,500 = 2.5463 = × (1 + (simple interest rate per period × 11))
2.5463 – 1 = 1.5463 = simple interest rate per period × 11
1.5463 / 11 = .07997 = 14.057% = simple interest rate per year
If Mona invests $19,500 in 1 year from today and earned simple interest of 14.057% per year, she