9.2 CALCULATING PRINCIPAL, RATE, AND TIME
9.2
CALCULATING PRINCIPAL, RATE,
AND TIME PERIOD
By re-arranging the simple interest formula, I = Prt, we can find the required value.
EXAMPLE 9.2A
If the simple interest amount charged on a loan was $250 and the interest rate was 8.5% p.a. for 15
months, what was the amount of principal borrowed?
SOLUTION
I = $250.00 r = 8.5% = 0.085 t = 15 months =
Re-arranging the simple interest formula, I = Prt, P=
15
years
12
250.00
I
=
= $2,352.94
15
rt
0.085 ×
12
EXAMPLE 9.2B
What will the annual interest rate be for $5,000 to earn $800 in 1.5 years?
SOLUTION
P = $5,000.00
I = $800.00 t = 1.5 years
Re-arranging the simple interest formula, I = Prt,
r=
I
800.00
=
= 0.106666... = 10.67% p.a.
Pt
5000.00 × 1.5
EXAMPLE 9.2C
How long will it take for $6,000 to earn $1,450 at 4.1% p.a. simple interest? Express your answer in
years and months, rounded up to the next month.
SOLUTION
P = $6,000.00 I = $1,450.00 r = 4.1% p.a. = 0.041
Re-arranging the simple interest formula, I = Prt, t=
1,450.00
I
=
6,000.00 × 0.041
Pr
= 5.894308... years
= 5 years and (0.894308... × 12) months
= 5 years and 10.731707... months
= 5 years and 11 months
137
CHAPTER 9 | SIMPLE INTEREST
EXERCISES 9.2 Answers to the odd numbered problems are available online
1.
I f Thomas borrowed $9,000 from a friend at 5.4% p.a. over 20 months, how much simple interest
does he owe?
2.
ivian lent her daughter $2,000 at 3.8% p.a. over 16 months. How much simple interest is she
V
owed?
3.
J enna borrowed a sum for 6 months at 4.6% p.a. If the interest he owed accumulated to $309.78,
what was the principal amount that he borrowed?
4.
arlos was owed $1,000 interest on an amount he lent for 11 months at 9% p.a. What was the
C
principal amount that he lent?
5.
If $2,600 earns $21 in 86 days, what is the annual interest rate?
6.
If $1,500 earns $17 in 75 days, what is the annual interest rate?
7.
I f Ghulam wants to earn an interest of $1,345 on a $10,000 investment for 2.5 years, what rate of
simple interest does he require?
8.
I f Tatiana wants to pay no more than $1,600 in interest on a loan of $17,000 that he has taken for
1.5 years, what is the maximum simple interest rate he can agree on?
9.
How many days will it take $2,900 to earn $43.55 at 17% p.a.?
10. How many days will it take for $7,000 to earn $700 at 10% p.a.?
11. How long will it take for $1,000 to earn $400 at 8% p.a.? Express your answer in years and months,
rounded up the next month.
12. How long will it take for $3,000 to earn $520 at 8% p.a.? Express your answer in years and months,
rounded up the next month.
13. Find the annual rate of simple interest needed for $20,000 to earn $4,345 in 3.5 years.
14. Find the annual rate of simple interest needed for $14,000 to earn $2,765 in 2.5 years.
9.3
CALCULATING MATURITY VALUE
The maturity value (S), also called future value, is the sum of the principal and interest.
S=P+I
Substituting the simple interest formula, I = Prt, in the above formula,
138
S = P + Prt
Therefore, S = P(1 + rt)
Re-arranging, we get, P=
S
1 + rt