QT – Nov 2015 – L1 – Q5b – Mathematics of Business Finance

Determine how long it will take for an investment to grow at a given interest rate and calculate the interest rate required for tripling the investment.

Question

KuKu invested GHS 2000.00 into a Deluxe Equity Fund.

Required:
(i) Determine how long it will take for the GHS 2000.00 investment to accumulate GHS 800.00 interest at 10% compounded quarterly, if the interest is allowed for the fractional part of a conversion period (1 month = 30 days).

(ii) Determine how long it will take the GHS 2000.00 investment to triple in value if it doubled in value in 6 years at a certain rate of interest compounded monthly (1 month = 30 days).
(iii) Determine the interest rate in (ii).

Answer

(i) Time to accumulate GHS 800 interest at 10% compounded quarterly:

To calculate how long it will take for the GHS 2000 investment to accumulate GHS 800 interest at 10% compounded quarterly, we use the compound interest formula:

$A = P (1 + n r)^{n t}$

Where:

$A = 2800$ (GHS 2000 + GHS 800)
$P = 2000$
$r = 0.10$ (10%)
$n = 4$ (quarterly compounding)
Solve for

Taking logarithms:

Therefore, it will take approximately 3 years, 4 months, and 11 days for the investment to accumulate GHS 800 interest.

(ii) Time to triple in value if it doubles in 6 years:

If the GHS 2000 investment doubled in value in 6 years, it means the new value after 6 years is GHS 4000. To determine how long it will take for the investment to triple (GHS 6000), we use the same compound interest formula.

Let the time it takes to double be $t = 6$ years and let the time to triple be $t_3$ . We know the investment doubles in 6 years, so the interest rate is compounded monthly. Let $r$ be the interest rate.