Last Updated on September 6, 2026 by Maged kamel
A solved problem for compound interest.
Detailed Expression for continuous compounding
This is the equation used to estimate the future value of continuously compounded payments, where (e) is Euler’s number. We will need to use the equation for the third option in the next solved problem, as we will see later on.
A solved problem; the reference is “Time Value of Money, Part 1.“
Select the correct option from the four given options: the least amount to be deposited today to reach $10000 after the given number of years from today. The interest rate options vary by interest rate and by interest frequency.
Option 1: the solved problem for compound interest.
This is the first option. How do we find the present value P0 to receive $10,000 after 4 years at 8% interest, compounded quarterly?
The relation P0 = F* (P/F,i%,n) will be used, provided that the new interest rate is adjusted to (0.08/4). The term (1+i/n)^nt=(1+(0.08/4))^(4*4), since the number of years=4, the present value=F/(1+i/n)^nt=10,000/(1+0.02)^(4*4)=$7284.45.
Option 2 for the solved problem for compound interest.
This is the second option: how to find the present value P0 to get $10,000 after 5 years at an interest rate of 7% compounded yearly?
The relation P0 = F* (P/F) ^i% will be used, provided that the new interest rate is. The term (1+i/n)^nt=(1+(0.07/1))^(1*5), since the number of years=5, the present value=F/(1+i/n)^nt=10,000/(1+0.07)^(5)=$7192.86.
Option 3 for the solved problem for compound interest.
This is the third option: how to find the present value P0 required to reach $10,000 after 10 years at an interest rate of 4% compounded continuously?
The relation P0 = F*(P/F, i%, n) will be used, provided that the new interest rate is, and the Euler value e is taken as 2.7183; it is the factor for continuous compounding.The term (e)^it=(2.718))^(0.04*10), since the number of years=10, the present value=F/(e^)it=10,000/(2.718))^(0.04*10)=$6703.1825.
Option 4 for the solved problem for compound interest.
This is the fourth option: how to find the present value P0 to get $10,000 after 8 years at 4% interest, compounded semiannually.
The relation P0 = F*P/F, i%, n) will be used, provided that the new interest rate is 4%, compounded semiannually.The term (1+i/n)^nt=(1+(0.04/2))^(2*8), since the number of years=8, the present value=F/(1+i/n)^nt=10,000/(1+0.02)^(16)=$7284.458.
Among the options, the lowest P0 value is $ 6703.2, corresponding to option C.
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For a valuable external resource, Engineering Economy is a good reference.
The next post is Post 7– Approach to Uniform series of compound interest-1/2.