Download CALCULATING MATURITY VALUE

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
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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
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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,
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S = P + Prt
Therefore, S = P(1 + rt)
Re-arranging, we get, P=
S
1 + rt
9.3 CALCULATING MATURITY VALUE
EXAMPLE 9.3A
Find the maturity value (accumulated value) for an investment of $10,000 for 10 months at
6.7% p.a. simple interest.
SOLUTION
P = $10,000.00
r = 6.7% p.a. = 0.067
S = P(1 + rt) = 10,000 (1 + 0.067 ×
EXAMPLE 9.3B
t = 10 months =
10
years
12
10
) = 10,000 (1.05583333) = $10,558.33
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What is the principal (or present value) that will grow to $12,500 in 2 years at a simple interest rate of
5% p.a.
SOLUTION
S = $12,500.00
P=
r = 5% = 0.05
t = 2 years
S
12,500.00
=
= $11,363.64
1 + rt
1 + 0.05 × 2
EXERCISES 9.3 Answers to the odd numbered problems are available online
1.
ichael invested $5,600 for 200 days at an interest rate of 4% p.a. Calculate the maturity value of
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his investment.
2.
ebecca borrowed $2,800 for 150 days at simple interest of 3% p.a. Calculate the maturity value
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of the loan.
3.
amza borrowed $10,900 for 14 months at 6.4% p.a. to take care of his expenses while his new
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business became profitable. What is the maturity value of his debt?
4.
Svetlana lent a friend $4,000 for 18 months at 5.5% p.a. What is the maturity value of the loan?
5.
What is the principal amount that will mature to $5,000 in 1 year at an interest rate of 6.2% p.a.?
6.
What is the principal amount that will mature to $7,500 in 2 years at an interest rate of 4.5% p.a.?
7.
What is the principal amount that will mature to $10,000 in 91 days at an interest rate of 5.6% p.a.?
8.
What is the principal amount that will mature to $13,500 in 182 days at an interest rate of 6.2% p.a.?
9.
Gonzalo invested $3,000 for 120 days at 5.4% p.a. What is the future value of his investment?
10. Karishma borrowed $5,000 for 145 days at 4.6% p.a. What is the future value of the loan?
11. What is the accumulated value of $1,900 after 14 months at 7.4% p.a.?
12. What is the accumulated value of $1,200 after 18 months at 5.3% p.a.?
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