Answer :
The amount of money Rashon would need to invest is equal to $8,300.46.
How to determine the value of equivalent quarterly interest rate?
Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:
A(t) = P(1 + r/n)^{nt}
Where:
- A represents the future value.
- r represents the interest rate.
- n represents the number of times compounded.
- P represents the principal.
- T represents the time measured in years.
In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.
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Answer:
In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:
Quarterly interest rate = 0.069/4
Quarterly interest rate = 0.01725%
20,200 = P(1 + 0.01725)^{4 × 13}
20,200 = P(1.01725)^52
20,200 = 2.4336P
Principal, P = 20,200/2.4336
Principal, P = $8,300.46.